Center of quantum group in roots of unity and the restriction of integrable models

量子计算中英文2019英文FROM BITS TO QUBITS, FROM COMPUTING TO QUANTUM COMPUTING: AN EVOLUTION ON THE VERGE OF A REVOLUTION IN THE COMPUTINGLANDSCAPEPi rjan Alexandru; Petroşanu Dana-Mihaela.ABSTRACTThe "Quantum Computing" concept has evolved to a new paradigm in the computing landscape, having the potential to strongly influence the field of computer science and all the fields that make use of information technology. In this paper, we focus first on analysing the special properties of the quantum realm, as a proper hardware implementation of a quantum computing system must take into account these properties. Afterwards, we have analyzed the main hardware components required by a quantum computer, its hardware structure, the most popular technologies for implementing quantum computers, like the trapped ion technology, the one based on superconducting circuits, as well as other emerging technologies. Our study offers important details that should be taken into account in order to complement successfully the classical computer world of bits with the enticing one of qubits.KEYWORDS: Quantum Computing, Qubits, Trapped Ion Technology, Superconducting Quantum Circuits, Superposition, Entanglement, Wave-Particle Duality, Quantum Tunnelling1. INTRODUCTIONThe "Quantum Computing" concept has its roots in the "Quantum Mechanics" physics subdomain that specifies the way how incredibly small particles, up to the subatomic level, behave. Starting from this concept, the Quantum Computing has evolved to a new paradigm in the computing landscape. Initially, the concept was put forward in the 1980s as a mean for enhancing the computing capability required tomodel the way in which quantum physical systems act. Afterwards, in the next decade, the concept has drawn an increased level of interest due to the Shor's algorithm, which, if it had been put into practice using a quantum computing machine, it would have risked decrypting classified data due to the exponential computational speedup potential offered by quantumcomputing [1].However, as the development of the quantum computing machines was infeasible at the time, the whole concept was only of theoretical value. Nowadays, what was once thought to be solely a theoretical concept, evolved to become a reality in which quantum information bits (entitled "qubits") can be stored and manipulated. Both governmental and private companies alike have an increased interest in leveraging the advantages offered by the huge computational speedup potential provided by the quantum computing techniques in contrast to traditional ones [2].One of the aspects that make the development of quantum computers attractive consists in the fact that the shrinkage of silicon transistors at the nanometer scale that has been taking place for more than 50 years according to Moore's law begins to draw to a halt, therefore arising the need for an alternate solution [3].Nevertheless, the most important factor that accounts for boosting the interest in quantum computing is represented by the huge computational power offered by these systems and the fact that their development from both hardware and software perspectives has become a reality. Quantum computing managed to surpass the computability thesis of ChurchTuring, which states that for any computing device, its power computation could increase only in a polynomial manner when compared to a "standard" computer, entitled the Turing machine [4].During the time, hardware companies have designed and launched "classical" computing machines whose processing performance has been improving over the time using two main approaches: firstly, the operations have been accelerated through an increased processing clock frequency and secondly, through an increase in the number of operations performed during each processing clock's cycle [5].Although the computing processing power has increased substantially after having applied the above-mentioned approaches, the overall gain has remained inaccordance with the thesis of Church-Turing. Afterwards, in 1993, Bernstein and Vazirani have published in [6] a theoretical analysis stating that the extended Church-Turing thesis can be surpassed by means of quantum computing. In the following year, Peter Shor has proved in his paper that by means of quantumcomputing the factorization of a large number can be achieved with an exponentially computing speedup when compared to a classical computing machine [7-9]. Astonishing as the theoretical framework was, a viable hardware implementation was still lacking at the time.The first steps for solving this issue have been made in 1995, when scientists have laid the foundations for a technology based on a trapped ion system [10] and afterwards, in 1999, for a technology employing superconducting circuits [11]. Based on the advancement of technology, over the last decades, researchers have obtained huge progress in this field, therefore becoming able to build and employ the first quantum computing systems.While in the case of a classical computing machine the data is stored and processed as bits (having the values 0 or 1), in the case of a quantum computingmachine, the basic unit of quantum information under which the data is stored and processed is represented by the quantum bits, or qubits that can have besides the values of 0 and 1, a combination of both these values in the same time, representing a "superposition" of them [12].At a certain moment in time, the binary values of the n bits corresponding to a classical computer define a certain state for it, while in the case of a quantumcomputer, at a certain moment in time, a number of n qubits have the possibility to define all the classical computer's states, therefore covering an exponential increased computational volume. Nevertheless, in order to achieve this, the qubits must be quantum entangled, a non-local property that makes it possible for several qubits to be correlated at a higher level than it was previously possible in classical computing. In this purpose, in order to be able to entangle two or several qubits, a specific controlled environment and special conditions must be met [13].During the last three decades, a lot of studies have been aiming to advance thestate of knowledge in order to attain the special conditions required to build functional quantum computing systems. Nowadays, besides the most popular technologies employed in the development of quantum computing systems, namely the ones based on trapped ion systems and superconducting circuits, a wide range of other alternative approaches are being extensively tested in complex research projects in order to successfully implement qubits and achieve quantum computing [14].One must take into account the fact that along with the new hardware architectures and implementations of quantum computing systems, new challenges arise from the fact that this new computing landscape necessitates new operations, computing algorithms, specialized software, all of these being different than the ones used in the case of classical computers.A proper hardware implementation of a quantum computing system must take into account the special properties of the quantum realm. Therefore, this paper focuses first on analyzing these characteristics and afterwards on presenting the main hardware components required by a quantum computer, its hardware structure, the most popular technologies for implementing quantum computers, like the trapped ion technology, the one based on superconducting circuits, as well as other emerging technologies. Our developed research offers important details that should be taken into account in order to complement successfully the classical computer world of bits with the enticing one of qubits.2.SPECIAL PROPERTIES OF THE QUANTUM REALMThe huge processing power of quantum computers results from the capacity of quantum bits to take all the binary values simultaneously but harnessing this vast amount of computational potential is a challenging task due to the special properties of the quantum realm. While some of these special properties bring considerable benefits towards quantum computing, there are others that can hinder the whole process.One of the most accurate and extensively tested theory that comprehensibly describes our physical world is quantum mechanics. While this theory offers intuitive explanations for large-scale objects, while still very accurate also at the subatomiclevel, the explanations might seem counterintuitive at the first sight. At the quantum level, an object does not have a certain predefined state, the object can behave like a particle when a measurement is performed upon it and like a wave if left unmeasured, this representing a special quantum property entitled wave-particle duality [15].The global state of a quantum system is determined by the interference of the multitude of states that the objects can simultaneously have at a quantum level, the state being mathematically described through a wave function. Actually, the system's state is often described by the sum of the different possible states of its components, multiplied by a coefficient consisting in a complex number, representing, for each state, its relative weight [16, 17]. For such a complex coefficient, by taking into consideration its trigonometric (polar) form, one can write it under the form Aew = A(cos6 + i sind), where A > 0 represents the module of this complex number and is denoted as the "amplitude", while в represents the argument of the complex number, being denoted as "the phase shift". Therefore, the complex coefficient is known if the two real numbers A and в are known.All the constitutive components of a quantum system have wave-like properties, therefore being considered "coherent". In the case of coherence, the different states of the quantum components interact between them, either in a constructive manner or in a destructive one [1]. If a quantum system is measured at a certain moment, the system exposes only a single component, the probability of this event being equal to the squared absolute value of the corresponding coefficient, multiplied by a constant. If the quantum system is measured, from that moment on it will behave like a classical system, therefore leading to a disruption of its quantum state. This phenomenon causes a loss of information, as the wave function is collapsed, and only a single state remains. As a consequence of the measurement, the wave function associated to the quantum obj ect corresponds only to the measured state [1, 17].Considering a qubit, one can easily demonstrate that its quantum state could be represented by a linear superposition of two vectors, in a space endowed with a scalar product having the dimension 2. The orthonormal basis in this space consists of thevectors denoted as |0 >= [Jj and |1 >= [°j. If one considers two qubits, they could be represented as a linear combination of the 22 elements of the base, namely the ones denoted as .... Generally, in the case of n qubits, they could be represented by a superposition state vector in a space having the dimension 2n [2].Another special property of the quantum realm consists in the entanglement, a property that has the ability to exert a significant influence on quantumcomputing and open up a plethora of novel applications. The physical phenomenon of quantum entanglement takes place when two (or more) quantumobjects are intercorrelated and therefore the state of a quantum object influences instantaneously the state(s) of the other(s) entangled quantum object(s), no matter the distance(s) between these objects [16].Another important quantum mechanical phenomenon that plays a very important role in quantum computing is quantum tunneling that allows a subatomic particle to go through a potential barrier, which otherwise would have been impossible to achieve, if it were to obey only the physical laws of classical mechanics. An explanation of this different behavior consists in the fact that in quantum mechanics the matter is treated both as waves and particles, as we have described above, when we have presented the wave-particle duality concept [15].The Schrödinger equation describes the variation of the wave function, taking into account the energy environment that acts upon a quantum system, therefore highlighting the way in which this quantum system evolves. In order to obtain the mathematical description of the environment, of the energies corresponding to all the forces acting upon the system, one uses the Hamiltonian of the quantum system. Therefore, the control of a quantum system can be achieved by controlling its energy environment, which can be obtained by isolating the system from the external forces, and by subjecting the system to certain energy fields as to induce a specific behavior. One should note that a perfect isolation of the quantum system from the external world cannot be achieved, therefore in practice the interactions are minimized as much as possible. Over time, the quantum system is continuously influenced to a small extent by the external environment, through a process called "decoherence",process that modifies the wave function, therefore collapsing it to a certain degree [1].Figure 1 depicts the main special properties of the quantum realm, which, when precisely controlled, have the ability to influence to a large extent the performance of a quantum computer implementation, and open up new possibilities for innovation concerning the storing, manipulation and processing of data.In the following, we analyze a series of hardware components and existing technologies used for developing and implementing quantum computers.3.AN OVERVIEW OF THE NECESSARY HARDWARE AND OF THE EXISTING TECHNOLOGIES USED IN THE IMPLEMENTATIONS OF QUANTUM COMPUTERSA proper hardware architecture is vital in order to be able to program, manipulate, retrieve qubits and overall to achieve an appropriate and correct quantumcomputer implementation. When implementing a quantum computer at the hardware level, one must take into account the main hardware functions, a proper modularization of the equipment along with both similarities and differences between quantum and classic computer implementations. Conventional computers are an essential part in the successful implementation of a quantum computer, considering the fact that after having performed its computation, a quantumcomputer will have to interact with different categories of users, to store or transmit its results using classic computer networks. In order to be efficient, quantum computers need to precisely control the qubits, this being an aspect that can be properly achieved by making use of classic computing systems.The scientific literature [1, 18, 19] identifies four abstract layers in the conceptual modelling process of quantum computers. The first layer is entitled the "quantum data plane" and it is used for storing the qubits. The second layer, called "control and measurement plane", performs the necessary operations and measurement actions upon the qubits. The third layer entitled "control processor plane" sets up the particular order of operations that need to be performed along with the necessary measurement actions for the algorithms, while the fourth abstract layer, the "host processor", consists in a classical computer that manages the interface withthe different categories of personnel, the storage of data and its transmission over the networks.In the following, we present the two most popular technologies employed in the development of quantum computing systems, namely the ones based on trapped ion systems and superconducting circuits and, afterwards, other alternative approaches that are being extensively tested in complex research projects in order to successfully implement qubits and achieve quantum computing.By means of trapping atomic ions, based on the theoretical concepts presented by Cirac et al within [20], in 1995, Monroe et al [21] revealed the first quantumlogic gate. This was the starting point in implementing the first small scale quantum processing units, making it possible to design and implement a rich variety of basic quantum computing algorithms. However, the challenges to scale up the implementations of quantum computers based on the trapped ion technology are enormous because this process implies a synergy of complex technologies like coherent electronic controllers, laser, radio frequency, vacuum, microwave [1, 22].In the case of a quantum computer based on the trapped atomic ions technology, the qubits are represented by atomic ions contained within the quantum data plane by a mechanism that keeps them in a certain fixed location. The desired operations and measurement actions are performed upon the qubits using accurate lasers or a source of microwave electromagnetic radiation in order to alter the states of the quantum objects, namely the atomic ions. In order to reduce the velocity of the quantum objects and perform measurements upon them, one uses a laser beam, while for assessing the state of the ions one uses photon detectors [14, 23, 24]. Figure 2 depicts an implementation of the quantum trapping atomic ions technology.Another popular technology used in the development and implementation of quantum computers is based on superconducting quantum circuits. These quantum circuits have the property of emitting quantized energy when exposed to temperatures of 10-3K order, being referred in the literature as "superconducting artificial atoms" [25]. In contrast to classic integrated circuits, the superconducting quantum circuits incorporate a distinctive characteristic, namely a"Josephson junction" that uses wires made of superconducting materials in order to achieve a weak connection. The common way of implementing the junction consists in using an insulator that exposes a very thin layer and is created through the Niemeyer-Dolan technique which is a specialized lithographic method that uses thin layers of film in order to achieve overlapping structures having a nanometer size [26].Superconducting quantum circuits technology poses a series of important advantages, offering red3uced decoherence and an improved scale up potential, being compatible with microwaves control circuits, operating with time scales of the nanosecond order [1]. All of these characteristics make the superconducting quantum circuits an attractive and performant technique in developing quantum computers. A superconducting quantum circuit developed by D-Wave Systems Inc. is depicted in Figure 3.In order to overcome the numerous challenges regarding the scaling of quantum computers developed based on trapped ion systems and superconducting circuits, many scientists focus their research activity on developing emerging technologies that leverage different approaches for developing quantumcomputers.One of the alternatives that scientists investigate consists in making use of the photons' properties, especially of the fact that photons have a weak interaction between each other and also with the environment. The photons have been tested in a series of quantum experiments and the obtained results made the researchers remark that the main challenge in developing quantum computers through this approach is to obtain gates that operate on spaces of two qubits, as at the actual moment the photons offer very good results in terms of single qubit gates. In order to obtain the two-qubit gates, two alternative approaches are extensively being investigated as these have provided the most promising results.The first approach is based on operations and measurements of a single photon, therefore creating a strong interaction, useful in implementing a probabilistic gate that operates on a space of two qubits [1]. The second alternative approach employs semiconductor crystals structures of small dimensions in order to interact with the photons. These small structures can be found in nature, case in which they are called"optically active defects", but can also be artificially created, case in which they are called "quantum dots". An important challenge that must be overcome when analyzing quantum computers based on photons is their size. Until now, the development of this type of computers has been possible only for small dimensions, as a series of factors limit the possibility to increase the dimensions of photon quantum computers: the very small wavelengths of the photons (micron-size), their very high speed (the one of the light), the direction of their movement being along a certain dimension of the optical chip. Therefore, trying to significantly increase the number of qubits (represented by the photons) proves to be a difficult task in the case of a photonic device, much more difficult than in the case of other systems, in which the qubits are located in space. Nevertheless, the evolution of this emerging technology promises efficient implementations in the near future [27].Another technology that resembles the one of "trapping atomic ions" for obtaining qubits consists in the use and manipulation of neutral atoms by means of microwave radiation, lasers and optics. Just like in the case of the trapping atomic ions technology, the "cooling" process is achieved using laser sources. According to [1, 28], in 2018 there were implemented successfully quantum systems having 50 qubits that had a reduced space between them. By means of altering the space between the qubits, these quantum systems proved to be a successful analog implementation of quantum computers. In what concerns the error rates, according to [29], in 2018 there have been registered values as low as 3% within two-qubit quantum systems that managed to isolate properly the operations performed by nearby qubits. Since there are many similarities between the two technologies, the scaling up process faces a lot of the problems of the "trapping atomic ions" technology. However, the use of the neutral atoms technology offers the possibility of creating multidimensional arrays.A classification of semiconductor qubits is made according to the method used to manipulate the qubits that can be achieved either by photon manipulation or by using electrical signals. Quantum dots are used in the case of semiconductor qubits that are gated by optical means in order to assure a strong coupling of the photons while in the case of semiconductor qubits manipulated via electrical signals, voltages are usedupon lithographically metal gates for manipulating the qubits [1]. This quantum technology, although being less popular than other alternatives, resembles the existing classical electronic circuits, therefore one might argue that it has a better chance in attracting considerable investments that eventually will help speed up the scaling up process of quantum computers implementation.In order to scale up qubits that are optically gated, one needs a high degree of consistency and has to process every qubit separately at the optical level. In [30], Pla et al. state that even if the qubits that are gated electrically can be very dense, the material related problems posed not long-ago serious quality problems up to single qubits gates level. Although the high density provided by this type of quantum technology creates opportunities for integrating a lot of qubits on a single processor, complex problems arise when one has to manipulate this kind of qubits because the wiring will have to assure an isolation of the control signals as to avoid interference and crosstalk.Another ongoing approach in developing quantum computers consists in using topological qubits within which the operations to be performed upon are safeguarded due to a microscopically incorporated topological symmetry that allows the qubit to correct the errors that may arise during the computing process [1]. If in the future this approach materializes, the computational cost associated with correcting the quantum errors will diminish considerably or even be eliminated altogether. Although this type of technology is still in its early stages, if someday one is able to implement it and prove its technical feasibility, the topological quantum computers will become an important part of the quantum computing landscape.4. CONCLUSIONSQuantum computing represents a field in a continuous evolution and development, a huge challenge in front of researchers and developers, having the potential to influence and revolutionize the development of a wide range of domains like the computing theory, information technology, communications and, in a general framework, regarding from the time perspective, even the evolution and progress of society itself. Therefore, each step of the quantum computers' evolution has thepotential to become of paramount importance for the humanity: from bits to qubits, from computing to quantum computing, an evolution on the verge of a revolution in the computing landscape.中文从比特到量子比特，从计算到量子计算：计算机革命的演变抽象“量子计算”的概念已发展成为计算领域的一个新范例，具有极大地影响计算机科学领域和所有利用信息技术的领域的潜力。

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第1篇Introduction:Quantum entanglement, one of the most intriguing and challenging concepts in quantum mechanics, has puzzled scientists for over a century. This phenomenon, where particles become interconnected regardless of the distance separating them, has far-reaching implications for our understanding of the universe and potential technological advancements. In this interview question, we will delve into the scientific principles of quantum entanglement, its experimental validations, and the potential applications it may offer in the future.Section 1: Introduction to Quantum Entanglement1.1 Definition of Quantum Entanglement:Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles become linked in such a way that the quantum stateof each particle cannot be described independently of the state of the others, even when the particles are separated by large distances.1.2 Historical Background:The concept of quantum entanglement was first introduced by Albert Einstein, Boris Podolsky, and Nathan Rosen in 1935 in their famous paper titled "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?" This paper, often referred to as the EPR paradox, sparked a debate on the completeness and interpretation of quantum mechanics.1.3 Quantum Mechanics and Classical Mechanics:Quantum entanglement is a quintessential feature of quantum mechanics, which fundamentally differs from classical mechanics. In classical mechanics, the state of a system is determined by the positions and velocities of its particles, while in quantum mechanics, particles exist in a probabilistic state until measured.Section 2: The Principles of Quantum Entanglement2.1 Superposition:Superposition is a fundamental principle of quantum mechanics, which states that a quantum system can exist in multiple states simultaneously. This principle allows particles to be entangled, as their combined state cannot be described by the state of each particle individually.2.2 Non-locality:Non-locality is the idea that quantum entangled particles can instantaneously affect each other's states, regardless of the distance separating them. This concept challenges the principle of locality in classical physics, which dictates that no physical influence can travel faster than the speed of light.2.3 Bell's Inequality:John Bell proposed an inequality in 1964 that sets a limit on the amount of non-local correlations that can exist between particles in classical physics. Quantum entanglement violates Bell's inequality, providing experimental evidence for the non-local nature of quantum mechanics.Section 3: Experimental Validations of Quantum Entanglement3.1 Alain Aspect's Experiment:In 1982, Alain Aspect conducted a groundbreaking experiment that confirmed the violation of Bell's inequality, providing strong evidence for quantum entanglement and non-locality. His experiment involved measuring the polarizations of photons emitted from a source and showed that the correlations between the photons exceeded the limits set byBell's inequality.3.2 Quantum Key Distribution (QKD):Quantum key distribution is a secure communication protocol that leverages the principles of quantum entanglement. It allows two parties to share a secret key with the guarantee that any eavesdropping can be detected. QKD has been experimentally demonstrated over long distances, such as satellite-based communication links.3.3 Quantum Computing:Quantum entanglement is a crucial resource for quantum computing, which aims to solve complex problems much faster than classical computers. Quantum computers use qubits, which are entangled particles, to perform calculations by exploiting superposition and interference.Section 4: Implications for Future Technologies4.1 Quantum Communication:Quantum entanglement has the potential to revolutionize communication by enabling secure, long-distance communication using QKD. This technology could be crucial for establishing secure networks and protecting sensitive information.4.2 Quantum Computing:Quantum entanglement is essential for the development of quantum computers, which have the potential to solve complex problems in cryptography, material science, and optimization. Quantum computers could also simulate quantum systems, leading to new discoveries in chemistry, physics, and biology.4.3 Quantum Sensing:Quantum entanglement can be used to enhance the sensitivity of quantum sensors, which have applications in various fields, including gravitational wave detection, quantum metrology, and precision measurement.Conclusion:Quantum entanglement, with its fascinating principles and experimental validations, has the potential to reshape our understanding of the universe and enable groundbreaking technological advancements. From secure communication to powerful quantum computers, the implications of quantum entanglement are vast and far-reaching. As scientists continue to explore this intriguing phenomenon, we can expect even more exciting developments in the field of quantum physics and its applications.第2篇Introduction:Quantum entanglement, one of the most fascinating and enigmatic phenomena in the realm of physics, has intrigued scientists and philosophers alike for decades. This interview delves into the depths of quantum entanglement, exploring its origins, implications, and potential applications. Dr. Emily Newton, a renowned quantum physicist, shares her insights and experiences in this field.Part 1: The Basics of Quantum EntanglementQuestion 1: Can you explain what quantum entanglement is and how it differs from classical entanglement?Dr. Newton:Quantum entanglement is a phenomenon in which two or more particles become interconnected, such that the quantum state of one particle instantaneously correlates with the state of another, regardless of the distance separating them. This correlation persists even when the particles are separated by vast distances, which defies the principles of classical physics.In classical entanglement, such as the entanglement of a pair of dice, the outcome of one die is independent of the other. If you roll a six on one die, it does not affect the outcome of the other die. However, in quantum entanglement, the particles are not independent; their quantum states are correlated in such a way that measuring one particle's state instantly determines the state of the other particle, regardless of the distance between them.Question 2: How was quantum entanglement discovered, and what were the early reactions to this phenomenon?Dr. Newton:Quantum entanglement was first predicted by Albert Einstein, Boris Podolsky, and Nathan Rosen in their famous EPR paradox paper in 1935.They proposed a thought experiment involving two entangled particlesthat seemed to violate the principle of locality, which states that no information can travel faster than the speed of light.The initial reaction to the EPR paradox was skepticism, with Einstein famously dismissing quantum entanglement as "spooky action at a distance." However, subsequent experiments, such as those conducted by John Bell in the 1960s, provided strong evidence in favor of quantum entanglement, leading to a paradigm shift in our understanding of the quantum world.Part 2: The Mechanics of Quantum EntanglementQuestion 3: What are the key factors that contribute to the formation of entangled particles?Dr. Newton:The formation of entangled particles is a result of their interaction during the process of measurement or preparation. For example, when two particles are created together in an entangled state, their quantum states become correlated due to their shared history. This correlationis a fundamental aspect of quantum mechanics and cannot be explained by classical physics.Another way to create entangled particles is through a process called entanglement swapping, where two particles are initially entangled with a third particle, and then the third particle is separated from thefirst two. This results in the first two particles becoming entangled with each other, even though they have never interacted directly.Question 4: Can you explain the concept of quantum superposition and how it relates to entanglement?Dr. Newton:Quantum superposition is the principle that a quantum system can existin multiple states simultaneously until it is measured. This is analogous to a coin spinning in the air, which can be either heads or tails until it lands on one side.In the context of entanglement, superposition plays a crucial role. When two particles are entangled, their combined quantum state is a superposition of the individual states of each particle. This means that the particles can exhibit non-local correlations that are not determined until a measurement is made.Part 3: The Implications of Quantum EntanglementQuestion 5: How does quantum entanglement challenge our understanding of the universe?Dr. Newton:Quantum entanglement challenges our classical understanding of the universe in several ways. Firstly, it defies the principle of locality, which has been a cornerstone of physics for centuries. The idea that particles can instantaneously influence each other across vast distances suggests that the fabric of space-time may not be as fixed as we once thought.Secondly, quantum entanglement raises questions about the nature of reality itself. If particles can be correlated in such a way that their states are instantaneously connected, it challenges the idea that objects have definite properties independent of observation.Question 6: Are there any practical applications of quantum entanglement?Dr. Newton:Yes, there are several potential applications of quantum entanglement. One of the most promising is in quantum computing, where entangled particles can be used to perform complex calculations at speeds unattainable by classical computers. Quantum entanglement is also essential for quantum cryptography, which can be used to create unbreakable encryption methods.Moreover, entanglement has been used in quantum teleportation, where the state of a particle can be transmitted instantaneously from one location to another, potentially leading to new communication technologies.Conclusion:Quantum entanglement remains one of the most intriguing and challenging phenomena in physics. Dr. Emily Newton's insights into the mechanics and implications of this phenomenon provide a deeper understanding of the quantum world and its potential applications. As we continue to explore the mysteries of quantum entanglement, we may uncover new ways to harness its power and reshape our understanding of the universe.第3篇IntroductionQuantum entanglement, one of the most intriguing and mysterious phenomena in the field of quantum mechanics, has captured the imagination of scientists and the public alike. This question invites candidates to delve into the concept of quantum entanglement, its underlying principles, experimental demonstrations, and the potential implications it holds for future technology.Part 1: Introduction to Quantum Entanglement1.1 Definition and Basic PrinciplesQuantum entanglement refers to a phenomenon where two or more particles become interconnected in such a way that the quantum state of each particle cannot be described independently of the state of the others, even when they are separated by large distances. This correlation persists regardless of the distance between the particles, which challenges our classical understanding of locality and separability.1.2 Historical ContextThe concept of quantum entanglement was first introduced by Albert Einstein, Boris Podolsky, and Nathan Rosen in their famous EPR paradox paper in 1935. They described entanglement as "spooky action at a distance," suggesting that it defied the principles of local realism. However, subsequent experiments and theoretical developments have confirmed the reality of entanglement.Part 2: Theoretical Underpinnings of Quantum Entanglement2.1 Quantum SuperpositionQuantum superposition is a fundamental principle of quantum mechanics that allows particles to exist in multiple states simultaneously. This principle is crucial for understanding entanglement, as it enables particles to become correlated in a way that is not possible inclassical physics.2.2 Quantum Correlation and EntanglementQuantum entanglement arises from the non-classical correlations between particles. When particles become entangled, their quantum states become linked, and the state of one particle instantaneously influences the state of the other, regardless of the distance separating them.2.3 Bell's TheoremJohn Bell formulated a theorem in 1964 that demonstrated the incompatibility of quantum mechanics with local realism. Experimentsthat violate Bell's inequalities have confirmed the existence of quantum entanglement and its non-local nature.Part 3: Experimental Demonstrations of Quantum Entanglement3.1 Bell Test ExperimentsBell test experiments have been conducted to test the predictions of quantum mechanics and to demonstrate the non-local nature of entanglement. These experiments involve measuring the properties of entangled particles and analyzing the correlations between them.3.2 Quantum Key Distribution (QKD)Quantum Key Distribution is a protocol that uses quantum entanglement to securely transmit cryptographic keys. It takes advantage of theprinciple that any attempt to intercept the entangled particles will disturb their quantum state, alerting the communicating parties to the presence of an eavesdropper.3.3 Quantum TeleportationQuantum teleportation is the process of transmitting the quantum state of a particle from one location to another, without the particle itself traveling through the space between them. This phenomenon has been experimentally demonstrated and has implications for quantum computing and communication.Part 4: Implications for Future Technology4.1 Quantum ComputingQuantum computing, which relies on the principles of quantum mechanics, has the potential to revolutionize computing by solving certain problems much faster than classical computers. Quantum entanglement plays a crucial role in quantum computing, as it allows for the creation of qubits that can exist in multiple states simultaneously, enabling parallel processing.4.2 Quantum CommunicationQuantum communication utilizes the principles of quantum entanglement and superposition to achieve secure communication and distributed computing. Technologies like QKD and quantum teleportation are expected to transform the field of secure communication and enable new forms of data transmission.4.3 Quantum Sensors and MetrologyQuantum sensors and metrology techniques leverage the precision and sensitivity of quantum entanglement to measure physical quantities with unprecedented accuracy. This has applications in fields such as precision navigation, gravitational wave detection, and quantum simulation.ConclusionQuantum entanglement, with its counterintuitive nature and profound implications, remains a captivating and challenging subject in the field of quantum mechanics. As scientists continue to explore and harness thepower of entanglement, we can expect to see significant advancements in technology, leading to new possibilities in computing, communication, and metrology. This question has provided an opportunity to delve into the fascinating world of quantum entanglement and its potential future impact on society.。

美国，旧金山，Cupertino市，苹果公司新园区/福斯特事务所乔布斯的苹果公司的新园区，由福斯特事务所、ARUP美国公司和一家本地的Kier & Wright工程公司一同设计。

它靠近苹果现有的园区，与硅谷的其它公司，如eBay, Nvidia, Cisco, Netflix and Sun近邻。

该园区的功能如下：办公，研究，面积大约280万平方英尺，可容纳13000雇员，1000座位的会议厅，中心绿地。

相应的停车位。

它是一个令人着迷的建筑。

它像一个着陆的宇宙飞船。

它的中心帅称宽阔的内院。

这样的建筑并不便宜，它没有一块玻璃是平的，我们事务所在世界各地都有建成的建筑，我们能找到建筑用的最大的玻璃，我们想通过这种方式让建筑独特，这非常酷。

圆形有利于园区的安全保卫，也能促进内部的交流。

该项目通过产生电力来减低能耗。

为苹果公司的雇员们提供中央的开放绿地。

通过精心的设计，超越了经济社会和环境的局限。

乔布斯选择了正确的设计事务所。

从图纸上看，该项目正在等待城市当局审批，该项目很可能获得批准，可能于2015年落成。

原文：The city of Cupertino has released more details about the new Apple Campus, revealed back in June.The new documents confirm Foster + Partners as the architects, working with ARUP North America and Kier & Wright, a local civil engineering firm that has worked on Apple’s current campus and buildings for other tech companies (eBay, Nvidia, Cisco, Netflix and Sun, among others).About the program:An Office, Research and Development Building comprising approximately 2.8 million square feet for up to 13,000 employeesA 1,000 seat Corporate AuditoriumA Corporate Fitness CenterResearch Facilities comprising approximately 300,000 square feetA Central PlantAssociated ParkingIt’s a pretty amazing building. It’s a little like a spaceship landed. It’s got this gorgeous courtyard in the middle… It’s a circle. It’s curved all the way around. If you build things, this is not the cheapest way to build something. There is not a straight piece of glass in this building. It’s all curved. We’ve used our experience making retail buildings all over the world now, and we know how to make the biggest pieces of glass in the world for architectural use. And, we want to make the glass specifically for this building here. We can make it curve all the way around the building… It’s pretty cool.The round shape has also been cited as an important part of the campus’ security (better perimeter control) and to improve internal circulations.It’s interesting to see that the objectives of the project are focused on reducing the use of electricity by generating its own energy on an on-site Central Plant, provide open green spaces “for Apple employees’ enjoyment” and to “exceed economic, social, and environmental sustainability goals through integrated design and development”. It seems Jobs choose the right firms for this.By looking at the drawings it seems that the project is ready to go, and now it’s waiting for city approval. The city has revealed that they are very likely to approve the project, so it seems everything is on route for an opening in 2015.。

Semiconductors:An IntroductionA crucial feature of the quantum-mechanical band theory of solids is that electrons in a crystal of any given material occupy well-defined quantum states, with discrete momentum and energy values(Kittel 1996)The interactions that arise between the different atoms in the crystal result in the grouping of these states into bands of allowed energies,with successive bands being separated from each other by forbidden energy gaps.Within this picture,the manner in which the valence electronsfill the energy bands is critical to understanding the electrical properties of the crystal.Metals are materials in which the uppermost energy band is only partially filled with electrons(Fig.1),and exhibit high conductivity since electrons may easily be accelerated into new momentum states by the application of even a small electricfield.Insulators,on the other hand,are materials in which the uppermost energy band is(almost) completelyfilled with electrons,and is separated from the lowest band of empty states by a large energy gap(in excess of several electron volts,Fig.1). These materials exhibit poor conductivity,since the large energy gap that separates the valence band(the highestfilled band at low temperatures)from the conduction band(the lowest unfilled band at low temperatures)blocks the acceleration of electrons into new momentum states.A group of materials whose properties are intermediate between these two extremes is referred to as semiconductors.Thefilling of electron states in semiconductors is similar to that in insulators,except the valence and conduction bands are separated by a smaller energy gap,of order1–2eV.At absolute zero,their valence band is completelyfilled with electrons,while the conduction band is empty,and the electrical char-acteristics are therefore similar to those of insulators. With increasing temperature,however,increasing numbers of electrons are thermally excited across the energy gap,into the conduction band,and the conductivity increases(Fig.1).Since the number of electrons in the conduction band increases exponen-tially with temperature(see the discussion below),the conductivity of these materials exhibits very strong temperature dependence.The existence of the forbidden energy gap in semiconductors has allowed the development of a variety of optoelectronic devices,among which include light-emitting diodes,photodetectors,and solar cells,and diode and heterojunction lasers. Another critical feature of these materials is that, unlike in metals,their electrical properties may be modified over a wide range of parameter space by the controlled addition of impurities known as dopants.In pure silicon at room temperature,the intrinsic carrier concentration is approximately 1010cmÀ3,and may easily be varied by many orders of magnitude by doping with the appropriate impurity.Moreover,simply through the choice of dopant,it is possible to realize semiconductor systems in which the majority carriers are either negatively charged electrons,or positively charged holes.Thisflexibility in turn allows the realization of a range of novel,nonlinear,semiconductor devices, such as pn junctions,field-effect transistors(MOS-FETs and MESFETs),and bipolar junction transis-tors,and provides the basis for modern low-power (CMOS)electronics.The purpose of this article is to review the key concepts required for understanding the electrical properties of semiconductors.We begin with a discussion of the different types of semiconductors, their crystal structures,and their energy gaps.After this,we explain the bandstructure details of selected semiconductors(Si and GaAs),followed by a brief discussion of semiconductor statistics.It is here that we introduce the concept of holes as another source of charge carriers in semiconductors.In Sect.4,we discuss how doping may be utilized to modify the intrinsic carrier concentrations in semiconductors, and a brief summary is given in Sect.5.1.Elemental and Compound Semiconductors Broadly speaking,semiconductors may be divided into two distinct groups,namely elemental or compound semiconductors.As the name suggests,elemental semiconductors are formed from single chemical elements,and important members of this family include Si and pound semiconductors represent the largest group,however,and are formed as a result of the chemical reaction between two or more different elements (examples include GaAs,InAs,InP,and GaN).Another important group of materials is provided by semiconductor alloys ,among which include Al x Ga 1Àx As and Si 1Àx Ge x .These materials are compound semiconductors in which the atoms are arranged in a well-defined crystal structure,but in which the different chemical species are randomly distributed throughout this crystal.While the bonding in most semiconductors is largely covalent in nature,in compound semiconductors formed from elements other than those in Group IV of the periodic table,the bonding also exhibits a small ionic nature and the material is said to be polar (Ferry 1991).Elemental semiconductors,on the other hand,are referred to as nonpolar .Crystal structure plays an important role in determining the bandstructure,and the resulting electrical properties,of semiconductors.The vast majority of these materials exhibit either the diamond or the zincblende crystal forms (Fig.2),the under-lying lattice of which is the face-centered cubic lattice.In a compound semiconductor,such as GaAs,the two atoms in the basis are from different chemical species and this is known as the zincblende form.In either case,hybridization of the outermost occupied s -and p -orbitals gives rise to a tetrahedral bondingarrangement in the crystal (Ferry 1991)(Fig.2),in which each atom bonds to its four nearest neighbors,forming a tetrahedral structure with the center atom located at the body of the tetrahedron.While the diamond and zincblende structures account for the majority of semiconductors encoun-tered in nature,a less common form is the wurtzite structure.This is essentially based on the hexagonal lattice.The tetrahedral bonding arrangement remains in this crystal form,and GaN is an important example of a semiconductor that can exhibit the wurtzite structure.The crystal structure,and value of the principal energy gap ðE g Þ,of a number of different semiconductors are summarized in Table 1.The form of the principal gap (direct versus indirect)is also shown in this table,although we defer a discussion of this issue until Sect.2.1.2.Semiconductor BandstructureBandstructure diagrams are the key to understanding the electrical and optical properties of semiconduc-tors.These diagrams show the relationship between the electron energy and momentum,for different principal directions within the crystal.(Strictly speaking,the diagrams show the variation of the energy with electron wave vector k ,which is in turn related to the crystal momentum ,_k .See Singh (1993)for example.)While a number of techniques are available for the calculation of bandstructures,these approaches may be broadly divided into two groups.The first group consists of methods which compute the bandstructure of the entire conduction and valence bands,and an important example of such an approach is provided by the tight-binding method .Figure 2Illustrations of the unit cell in the diamond (left)and zincblende (right)crystal structures.The solid lines between atoms in both figures represent chemical bonds.Note that,for the sake of clarity,chemical bonds extending outside the unit cell are not shown.In the case of the zincblende structure,the different colored balls represent atoms from different chemical species (for example,Ga and As in GaAs).2Semiconductors:An IntroductionThis starts from the orbital wave functions of the individual atoms,and computes the electron energy by considering the interaction of a center atom with its neighbors.The simplest approach is to consider only nearest-neighbor interactions,although higher accuracy can be achieved by extending this model to account for next-nearest neighbor interactions as well.The other group of bandstructure calculations consists of methods which only describe the bandstructure close to the edge of the energy gaps.The advantage of such approaches,among which include the kÁp method,is a reduction in the complexity of the problem,and an accurate description of the energy bands near the principal gaps can be achieved.This simplicity is achieved at the cost of generality,however,since it is not possible to extend such approaches over a wide range of parameter space.For detailed discussions of bandstructure-calculation approaches in semiconduc-tors,we refer the interested reader to books by Ferry (1991),Yu and Cardona(1996),Singh(1993),Ferry (2000),and Hamaguchi(2001).We have mentioned that bandstructure diagrams show the relationship between the electron energy and momentum for different principal directions within the crystal.These directions are defined in terms of the reciprocal lattice,which may be viewed as the Fourier transform of the real-space lattice of the crystal.Since the semiconductors of interest hereexhibit either the diamond or zincblende structures,it is worthwhile to take a few moments to consider the definition of the principal axes for these crystals.As was mentioned already,both of these structures are formed on the face-centered cubic lattice,the reciprocal lattice of which is the body-centered cubic lattice(Kittel1996).In Fig.3,we show thefirst Brillouin zone for the body-centered cubic lattice, and indicate the terminology used to identify the important directions of the reciprocal lattice.The surface of the Brillouin zone contains all electron wave vectors for which the Bragg condition for diffraction from some particular family of crystal planes is satisfied,and so for which an energy gap is expected in the bandstructure.The various points identified in Fig.3are of importance since they indicate directions of high crystal symmetry.2.1Silicon BandstructureIn Fig.4,we show the computed bandstructure diagram for Si.There are a number of important general features in this diagram that are worthy of emphasis.To begin with,on the horizontal axis,the variation of energy with wave vector is plotted as we start at the L point in the Brillouin zone,and then progress to the G,X,and U points,beforefinally returning to the G point.Next,we note that the series of curves shown in Fig.4may be roughly grouped into two sets of four,separated by a forbidden-gap region(shaded area),where no electron states are available.The reason for this grouping is quite simpleTable1Key semiconductors,their crystal structure,and energy-gap values.Note that the other form of C is graphite, which exhibits a hexagonal crystal structure and is a semimetal.Semiconductor Crystalstructure Gap type Energy gap(E g)at300K(eV)Si Diamond Indirect 1.124C Diamond Indirect 5.50SiC Zincblende Indirect 2.416Ge Diamond Indirect0.664AlN Wurtzite Direct 6.2AlP Zincblende Indirect 2.45AlAs Zincblende Indirect 2.153AlSb Zincblende Indirect 1.615GaN Wurtzite Direct 3.44GaP Zincblende Indirect 2.272GaAs Zincblende Direct 1.424GaSb Zincblende Direct0.75InAs Zincblende Direct0.354InSb Zincblende Direct0.230CdS Zincblende Direct 2.50CdSe Wurtzite Direct 1.751CdTe Zincblende Direct 1.475Source:Madelung(1996),Pierret(1996).Figure3Thefirst Brillouin zone of the face-centered cubic lattice.The various symbols are used to denote directions ofhigh symmetry in the crystal.3Semiconductors:An Introductionto understand;in the tight-binding model,the energy is calculated from a knowledge of the atomic wave functions,in particular the wave functions of the valence electrons.In practice,these wave functions are the s-and p-orbitals,and,with two atoms in the basis of the diamond or zincblende structures,a total of eight wave functions are used as the basis set for the calculations.The interaction between the orbitals on different atoms gives rise to a hybridization,as a result of which both the valence and the conduction bands exhibit s-orbital-like and p-orbital-like nature. In particular,it may be shown that the top of the valence band is predominantly derived from the p-type orbitals,while the bottom of the conduction band at G is largely s-orbital derived.This difference has important implications for the bandstructure near the top of the valence band,where the nonzero spin-orbit interaction of the p-like electrons lifts the degeneracy of the valence band at the G point.This effect is shown in greater detail in Fig.5,where we show how the spin-orbit effect gives rise to the split-off valence band.Note that there is usually no spin-splitting at the bottom of the conduction band,since these electron states are predominantly s-like in nature,and so are characterized by zero angular momentum.(A splitting of the conduction band can arise due to the effects of bulk-inversion asymmetry in polar crystals,although this effect is typically small in most semiconductors(Lommer et al.1988).)Si is an indirect semiconductor,since the maximum in its valence band and the minimum in its conduc-tion band are located at different wave vectors.The valence-band maximum is located at the G point, while the minimum in the conduction band is located about85%of the way towards the X point(see Fig.4).Due to the symmetry of theface-centered Semiconductors:An Introductioncubic lattice,six equivalent X points may be identified.At least for reasonably small variations of the wave vector away from the X point,the energy variation may be assumed to be parabolic and may be written in terms of two effective masses:E ¼_2k 2x2m L þ_2ðk 2y þk 2z Þ2m Tð1ÞHere,m n L and m nT are the longitudinal and transverse effective masses,respectively.In terms of the free electron mass,m o ,it is found that m n L ¼0:91m o and m nT ¼0:19m o .For a given reference energy for which Eqn.(1)is valid,we may therefore identify six constant energy surfaces ,which are centered around the X point (Fig.6).The asym-metric,cigar-like shape of these energy surfaces reflects the difference,noted above,in the long-itudinal and transverse effective masses near the X point.As we discuss in more detail below,at room temperature,electrons in semiconductors tend to lie close to the bottom of the conduction band,and in Si this leads to the ‘‘puddling’’of electrons in the six conduction-band minima.The cigar-like features shown in Fig.6may therefore be viewed as repre-senting the occupation of electron states in the conduction band of Si. 2.2Gallium-Arsenide BandstructureIn Fig.7,we show the computed bandstructurediagram for GaAs.There are some important differences with the bandstructure of Si,probably the most important of which is that GaAs is a direct semiconductor;the maximum in its valence band and the minimum in its conduction band are located at the same points in reciprocal space.Close to the bottom of the conduction band,the variation of the energy with wave vector may be approximated as:E ¼_2k 22m nð2Þwhere the electron effective mass is isotropic and takes the value m n ¼0:067m o .Another important feature of the bandstructure is the presence of satellite valleys in the conduction band,which are the local minima located at the X and L points (in Fig.7).The effective mass is very different in these valleys,from the usual electron mass in the minimum near the G point,and a dramatic reduction in mobility results when electrons are accelerated to sufficient energy by an applied electric field,to scatter into these satellite valleys.As can be seen in Fig.8,the spin-splitting of the valence band is significantly larger in GaAs than in Si.The separation of the split-off band from the top of the valence band is denoted by D so ,and in Si the value of this parameter is 44meV,while in GaAs it is 350meV.It is for this reason that the split-off band plays little role in transport inGaAs.Figure 6Constant-energy ellipsoids in silicon,associated with the six-fold-degenerate minimum in the conduction band.5Semiconductors:An Introduction2.3Some General Comments on Bandstructure(a)Energy gaps .The energy gaps listed in Table 1are the principal energy gaps for the different materials,that is they are the smallest energy gaps that separate the top of the valence band from the bottom of the conduction band.The relative location of the maximum and minimum in k -spaceisFigure 8A comparison of the valence bandstructure of GaAs and Si,showing that spin-orbit coupling leads to a larger splitting of the valence band in GaAs than in Si (reproduced from Hamaguchi 2001with permission).6Semiconductors:An Introductionimportant for determining the optical properties of semiconductors.In indirect semiconductors,the maximum and minimum occur at different points in k-space and direct transitions from the conduction band to the valence band have low probability.The reason for this is that when an electron drops from the conduction band to the valence band,and releases its excess energy in the form of a photon, the crystal momentum must be conserved.(We should remember that crystal momentum is only defined to within an arbitrary reciprocal-lattice wave vector.See K ittel1996,for example.)While the photon may carry a large amount of energy,its momentum relative to that of the electron is very small.Thus,the transition of the electron should leave its wave vector almost unchanged from its initial value—a requirement that cannot be satisfied in an indirect semiconductor.Here,a large change in crystal momentum is associated with a transition between the conduction-band maximum and the valence-band minimum,and this must be taken up by the simultaneous emission or absorption of a phonon.Since this photon–phonon emission has a low probability,indirect materials,such as Si,are poor choices for optical emitters.The energy gap of semiconductors varies weakly with temperature,typically decreasing with increas-ing temperature.In Si,for example,the size of the energy gap decreases by about0.07eV when the temperature is increased from20to400K.This corresponds to a relative change of roughly6%, compared to the value of the room-temperature gap (Madelung1996).There are a number of processes that contribute to the temperature-dependent varia-tion of the bandgap(Ridley1999),one of which is thermal expansion of the crystal.This weakens the overlap integrals of the orbitals on the different atoms,and so reduces the energy hybridization resulting from the overlap.Another effect is a thermal smearing of the background periodic poten-tial,created by the atom cores in the crystal.These effects may be accounted for by considering the influence of temperature on the electron–phonon interaction,which provides a contribution to the total energy of electrons in the crystal.The important point is that the process of exciting electrons into the conduction band corresponds to the breaking of bonds in the crystal,which in turn‘‘softens’’the vibrational modes of the atoms,by weakening the elastic restoring forces exerted between them.By lowering the energy of the vibrational modes in this manner,it is possible to show that the size of the bandgap is reduced with increasing temperature (Ridley1999).(b)Conduction and valence-band effective masses. Within the context of band theory,the effective mass of carriers in a crystal is understood to be related to the curvature of their energy bands in k-space.The starting point of this discussion is the expression for the crystal momentum of an electron in the crystal. Considering,for ease of development,a one-dimen-sional problem,the crystal momentum may be written as:p¼_k¼m n v gð3Þwhere m n is the electron effective mass and v g is the electron group velocity.This latter quantity may be written as:v g¼1_d Eð4ÞBy combining Eqns.(3)and(4)we thus arrive at the following expression for the effective mass(Ferry 2000):1m n¼1_kd Ed kð5ÞWe see from Eqn.(5)that the effective mass is related to the gradient of the energy bands in k-space,as mentioned just above.(The reader may be more used to the expression1=m n¼ð1=_2Þðd2E=d k2Þ,but this is only valid for parabolic bands!Eqn.(5)represents a more general form for the effective mass that is valid for any dispersion of E with k.We refer the reader to Ferry(2000)for a more detailed discussion of this point.)In Fig.9,we illustrate schematically the typical bandstructure of a semiconductor near its energy gap.The k-space origin in thisfigure corresponds to the G point,which is a high point of symmetry for the crystal.In the absence of spin-orbit coupling,the top of the valence band is expected to be three-fold degenerate,since this portion of the bandstructure is derived from the p-type orbitals,which are three-fold degenerate in the absence of any magnetic interac-tion.Spin-orbit coupling lifts this degeneracy,how-ever,by lowering the energy of the split-off band relative to the other two components(see Fig.9).The top of the valence band is then left two-fold degenerate at the G point,and we refer to these bands,which typically exhibit different degrees of curvature,as the light-and heavy-hole bands.Values of the valence-band effective masses are listed for a few semiconductors in Table2.While spin-orbit coupling typically leaves the conduction-band edge unaffected,we have seen that in indirect semiconductors,such as Si,it is necessary to introduce multiple effective masses,which compli-cates the calculation of physical quantities depen-dent on the effective mass.In Si,for example, one defines the density of states effective mass, m nd62=3ðm*2T m n LÞ1=3¼1:08m o.As we will see,this mass is used in the density of states to calculate the occupation of electron states atfinite temperatures.It7Semiconductors:An Introductionis also possible,however,to define the conductivity effective mass ,which is used in calculations of the electrical properties.To determine this mass,we note that,with the electric field applied in a particular direction,two valleys will exhibit the longitudinal mass while the other four will exhibit the transverse mass.The conductivity mass is then defined as (Ferry 1991):1n c ¼14T þ2L ¼1oð6ÞAnother indirect semiconductor is germanium,which exhibits eight equivalent conduction-band minima,located at the L points in the Brillouin zone (see Fig.3).The ellipsoids are characterized by theeffective masses m n T ¼0:082m o and m nL ¼1:64m o ,and the density of states effective mass is givenby m n d 42=3ðm *2T m n L Þ1=3¼0:56m o .Note the factor of four,rather than eight,that appears in this expression;this results since only half of each ellipsoid is contained within the Brillouin zone.The conductivity mass for Ge can also be calculated using the principles discussed above,yielding m n c ¼0:12m o .In many semiconductors,there is typically a proportional scaling of the conduction-band effective mass with the size of the energy gap,as we illustrate for selected semiconductors in Fig.10.This figure shows that larger-gap semiconductors exhibit heavier masses,and this basic scaling can be accounted for within the k Áp method,which uses perturbation theory to expand the bandstructure around the G point.This approach yields a conduction-band effective mass that is predicted to vary as:1m n ¼1m o þ2p cv 3m o 2E g Gþ1E g G þD soð7ÞIn this equation p cv is a momentum matrix element (Singh 1993,Ferry 2000,Ridley 1999)involving the conduction-and valence-band wave functions,E g G is the bandgap measured at the G point,and D so is the magnitude of the valence-band spin splitting.In Fig.10we show that the conduction-band mass of many semiconductors follow the approximate scaling of mass with bandgap suggested by Eqn.(7).Table 2Valence-band effective masses for selectedsemiconductors;m n l ,m n h ,and m nso denote the effective mass for the light-,heavy-,and split-off-bands,respectively.Semiconductor m n l =m o m n h =m o m n so =m o Si 0.150.540.23Ge 0.0430.280.095GaAS 0.080.510.15GaP 0.170.670.46InAs 0.0260.400.14InP0.120.600.12Semiconductors:An Introduction3.Carrier Statistics in Semiconductors3.1Electrons and HolesAt absolute zero,the valence band in any semicon-ductor isfilled completely with electrons while its conduction band is empty.At this temperature,the semiconductor therefore behaves like an insulator, since the large energy gap that separates the highest filled electron states from the lowest empty ones makes it difficult to accelerate electrons by applying a modest electricfield.The difference between insula-tors and semiconductors becomes apparent when the temperature is increased above zero,however,and the thermal energy allows for the excitation of increasing numbers of electrons across the small forbidden gap of semiconductors into the conduction band.Under such conditions,currentflow through the semiconductor becomes possible and the con-ductivity of these materials increases with increasing temperature,as more electrons are excited into the conduction band(Fig.11).Now consider the situation where a single electron is excited from a completelyfilled valence band,into the conduction band,leaving behind an unfilled electron state in the valence band.The presence of this empty state has critical consequences for current flow,since electrons in the valence band may now also carry an electrical current,in addition to the electron excited into the conduction band.An issue that arises here,concerns how to describe theflow of current due to carriers in the valence band,and this discussion leads us to introduce the concept of holes. The basic idea is that,in the presence of an applied electricfield E(we once again consider a one-dimensional problem for simplicity),each electron state experiences the same change in wave number:D k¼Àe t_Eð8Þwhere t is the usual relaxation time and the minus sign reflects the negative charge of the electron.Instead of following how the electricfield affects the momentum of the large number of electrons in the almost-filled valence band,however,it is instead more convenient to consider what happens to the single unoccupied electron state.On the basis of the discussion above,it should be clear that the applied field must change the wave vector of this state by:D k¼þe t_Eð9Þwhere the positive sign means that the response now looks like that of a particle with a positive charge,þe. This positively charged particle is referred to as a hole,and we emphasize that this concept is simply introduced for convenience.This does not mean that electrons in the valence band somehow possess a positive charge.Rather,what we are saying is that with a single electron missing from the valence band, the collective response of the remaining electrons to an applied electricfield looks just like that which we would expect for a single positively charged hole. While we have thus far considered the case of a single electron promoted out of the valence band,the concept of holes remains useful even when we begin to excite larger numbers of electrons into the conduction band.As we will see below,calculations of the electrical properties of semiconductors there-fore typically require that we consider the influence of both electrons in the conduction band and holes in the valence band.(a)Energy scale for holes.We have introduced the concept of the hole as a positively charged quasipar-ticle,which is useful when describing the response of an almost-filled valence band to an applied electric field.The hole results when an electron is excited from the valence band into the conduction band, either by utilizing the available thermal energy in the system,or by an optical process in which the electron absorbs the energy of an incident photon.A comparison of Eqns.(8)and(9)indicates that the hole possesses a positive charge,þe.Another important feature to note is that holes possess an inverted energy scale,that is,moving down in the valence band corresponds to increasing hole energy. The simple example shown in Fig.12serves to clarify the reason for this inverted energy scale.In this figure,we consider the situation where we use a photon to excite an electron from the valence band to the bottom of the conduction band(denoted by E c in Fig.12).On the left-hand side of thisfigure,we show the case where the electron initially occupies a state at the top of the valence band(denoted by E v).On the right-hand side,however,the electron is excited from a state lying further down in the valence band.Since thefinal energy of the electron,after the photon is absorbed,is the same in both cases,it is clear that a photon with a larger energy is required to induce theSemiconductors:An Introduction。

想要了解的事物英语作文There are so many things in this world that I want to understand better. From the smallest particles that make up the universe to the grandest mysteries of the cosmos, the sheer vastness of human knowledge and the unknown is both humbling and exhilarating. Every day, new discoveries are being made that expand the boundaries of what we know, and I find myself constantly in awe of the incredible complexity and beauty of our reality.One of the areas I'm most fascinated by is the field of quantum physics. The counterintuitive behaviors of subatomic particles, like the fact that they can exist in multiple states simultaneously, have always captivated me. I would love to gain a deeper understanding of concepts like quantum entanglement, wave-particle duality, and the uncertainty principle. How can particles that are separated by vast distances instantly influence each other? What is the true nature of reality at the most fundamental level? These are the kinds of questions that keep me up at night, pondering the very fabric of existence.At the same time, I'm also deeply interested in the workings of the human mind and consciousness. How do our brains process information and give rise to the rich inner experience of thoughts, emotions, and sensations? What is the relationship between the physical brain and the subjective self? The field of neuroscience has made incredible strides in mapping the neural pathways and mechanisms underlying various cognitive functions, but there is still so much we don't understand about the emergent phenomenon of consciousness.I'm also endlessly curious about the origins and evolution of life on our planet. How did the first self-replicating molecules arise from the primordial soup, and what were the key evolutionary steps that led to the incredible diversity of life we see today? What are the fundamental principles and mechanisms that drive the evolution of species, and how do they interact with the ever-changing environment? The more I learn about biology and the history of life, the more I realize how little we truly know about the origins and mechanics of the living world.Another area that fascinates me is the vastness of the cosmos and our place within it. The scale of the universe, with its billions of galaxies separated by unimaginable distances, is almost incomprehensible to the human mind. What is the true nature of space and time? How did the universe begin, and what is its ultimatefate? Will we ever unravel the mysteries of dark matter and dark energy, the enigmatic components that seem to make up the majority of the universe? The more we learn, the more questions arise, and I'm driven to understand our place in this grand cosmic tapestry.Of course, there are also countless aspects of the human experience that I wish I could understand better. What are the roots of human behavior, and how do our evolutionary and cultural histories shape the way we think and act? How do we form meaningful connections with others, and what are the psychological and neurological underpinnings of love, empathy, and social bonds? What is the nature of consciousness, and how do subjective experiences emerge from the physical brain? These are the kinds of deep, existential questions that captivate me and drive my curiosity.Ultimately, I believe that the pursuit of knowledge and understanding is one of the most noble and rewarding endeavors a human being can undertake. The more we learn about the world and the universe around us, the more we realize how much we still have to discover. And with each new insight, we gain a deeper appreciation for the incredible complexity and beauty of our reality. It is a never-ending journey of exploration and discovery, and I am honored to be a part of it. There is simply so much I want tounderstand, and I can't wait to continue on this wondrous path of learning and growth.。

计算机的发展英文稿作文Title: The Evolution of Computers。

Introduction:The evolution of computers has been one of the most transformative journeys in human history. From the humble beginnings of mechanical calculators to the powerful supercomputers of today, the progress in computing technology has reshaped every aspect of our lives. In this essay, we delve into the fascinating journey of computer development, tracing its milestones and exploring its future prospects.Early Beginnings:The roots of computing can be traced back to ancient times when humans used tools like the abacus for basic calculations. However, the true birth of modern computing can be attributed to the invention of the mechanicalcalculator by Blaise Pascal in the 17th century. This device paved the way for further advancements in computing machinery.The Turing Machine and Electronic Computers:The conceptual framework for modern computing was laid by Alan Turing in the 1930s with his theoretical model, the Turing machine. This theoretical concept provided the foundation for electronic computers that emerged in themid-20th century. The Electronic Numerical Integrator and Computer (ENIAC), developed in the 1940s, is often regarded as the first electronic general-purpose computer. ENIAC marked the beginning of the digital computing era, revolutionizing tasks ranging from complex calculations to code-breaking during World War II.The Birth of Personal Computers:The 1970s witnessed the advent of personal computers (PCs), which brought computing power to individuals and small businesses. Companies like Apple and IBM playedpivotal roles in popularizing PCs, making computing accessible to a broader audience. The introduction of graphical user interfaces (GUIs) in the 1980s further simplified computer usage, enabling users to interact with computers through icons and menus instead of complex commands.The Internet Age:The 1990s ushered in the era of the internet, transforming computers from standalone devices to interconnected nodes in a global network. The World Wide Web, developed by Tim Berners-Lee, revolutionized communication, commerce, and information dissemination. The proliferation of the internet led to the rise of e-commerce, social media, and digital entertainment, fundamentally altering the way we live, work, and interact with each other.Mobile Computing and Smart Devices:The 21st century witnessed the rise of mobile computing,marked by the proliferation of smartphones and tablets. These pocket-sized devices, equipped with powerful processors and high-speed internet connectivity, have become indispensable tools in our daily lives. Mobile apps have transformed how we access information, communicate, and entertain ourselves, blurring the lines between physical and digital realities.Artificial Intelligence and Machine Learning:In recent years, advances in artificial intelligence (AI) and machine learning have propelled computing to new frontiers. AI-powered technologies are revolutionizing industries such as healthcare, finance, and transportation, enabling computers to perform tasks that were once exclusive to human intelligence. From autonomous vehicles to virtual assistants, AI is reshaping our perception of what computers can achieve.The Future of Computing:Looking ahead, the future of computing promises evenmore exciting possibilities. Quantum computing, with its potential to solve complex problems at speeds unimaginable with classical computers, holds the key to breakthroughs in areas like drug discovery, cryptography, and climate modeling. Additionally, developments in biocomputing and neuromorphic computing could lead to computers that mimic the structure and functionality of the human brain, opening up new avenues for artificial intelligence and cognitive computing.Conclusion:The evolution of computers has been a remarkable journey, marked by continuous innovation and transformation. From the early mechanical calculators to the era of quantum computing, computers have become indispensable tools that shape the way we live, work, and interact with the world.As we stand on the cusp of a new technological revolution, the possibilities are boundless, and the only limit is our imagination.。

塔诺基量子力学第三卷英文回答：Quantum mechanics, as described in the third volume of the Tannocky series, is a fascinating and complex field of study. It deals with the behavior of particles at the quantum level, where classical physics no longer applies.In this realm, particles can exist in multiple states simultaneously and can exhibit wave-particle duality.One of the fundamental principles of quantum mechanicsis superposition. This concept states that a particle can exist in multiple states or positions at the same time. For example, imagine a particle that can be in either the "up"or "down" state. In classical physics, the particle wouldbe in one state or the other. However, in quantum mechanics, the particle can exist in a superposition of both states simultaneously. It is only when a measurement is made that the particle "chooses" one of the states.Another important principle in quantum mechanics is entanglement. This phenomenon occurs when two particles become linked in such a way that the state of one particle is dependent on the state of the other, regardless of the distance between them. This concept is often described using the famous thought experiment of two entangled particles, known as "spooky action at a distance." For example, if two entangled particles are in a superposition of "up" and "down" states, measuring one particle will instantaneously determine the state of the other particle, even if they are light-years apart.Quantum mechanics also introduces the concept of uncertainty, as described by Heisenberg's uncertainty principle. This principle states that certain pairs of physical properties, such as position and momentum, cannot both be precisely known at the same time. The more precisely one property is known, the less precisely the other can be known. This inherent uncertainty at the quantum level is a fundamental aspect of the nature of reality.Overall, quantum mechanics is a highly mathematical and abstract field, but its principles have been successfully applied in various technological advancements. For example, quantum computers utilize the principles of superposition and entanglement to perform calculations at a much faster rate than classical computers. Quantum cryptography also relies on the principles of quantum mechanics to ensure secure communication.中文回答：量子力学是塔诺基系列第三卷中描述的一个引人入胜且复杂的研究领域。

nature photonics 模板-回复the question: "What is the future of quantum communication?"Introduction:Quantum communication is a rapidly evolving field that utilizes the principles of quantum physics to transmit information securely and efficiently. It has the potential to revolutionize how we communicate, offering unparalleled security and increased processing power. In this article, we will explore the future of quantum communication and its implications for various industries.1. What is quantum communication?Quantum communication is the science of transmitting information through quantum systems, such as photons. Unlike classical communication, which relies on binary code (0s and 1s), quantum communication uses quantum states, such as superposition and entanglement, to encode and transmit information. This allows for secure communication, as any interception or eavesdropping would disturb the quantum state and be immediately detected.2. Current state of quantum communication:Currently, quantum communication is at a transformative stage,transitioning from theoretical studies to practical applications. Quantum key distribution (QKD), the most mature form of quantum communication, has been successfully demonstrated over long distances. Major breakthroughs in QKD have enabled practical implementations, highlighting the potential for secure communication networks.3. Advancements in quantum networks:The future of quantum communication lies in the development of quantum networks. These networks will connect various nodes, enabling secure communication across long distances. Researchers are working on developing quantum repeaters, which will extend the reach of quantum networks. These repeaters use entanglement swapping techniques to maintain the coherence of quantum states across long distances, overcoming the limitations of signal degradation.4. Integration with classical communication:The integration of quantum communication with classical communication systems is crucial for realizing practical applications. Hybrid systems, combining quantum and classical communication, will allow for seamless and efficient informationtransfer. Additionally, quantum communication can enhance classical communication channels by providing secure encryption and increased bandwidth.5. Quantum internet:The ultimate goal of quantum communication is to establish a quantum internet. This future network will support a wide range of applications, including secure communication, distributed quantum computing, and precision sensing. Researchers are actively exploring various approaches to building a quantum internet, such as using satellites for global coverage and employing quantum repeaters for long-distance communication.6. Applications of quantum communication:Quantum communication has the potential to revolutionize several industries. In the field of finance, quantum communication can provide secure transmission of financial data, protecting sensitive information from hacking attempts. In healthcare, quantum communication can facilitate secure transmission of medical records and support telemedicine. In the defense sector, quantum communication can enable secure military communication and enhance intelligence gathering capabilities.7. Challenges and future prospects:Despite the remarkable progress in quantum communication, several challenges remain. The development of reliable quantum repeaters and the creation of practical quantum memories are areas that require further research. Moreover, standardization of quantum communication protocols and technologies will be crucial for universal adoption. However, the future prospects of quantum communication are bright, with ongoing research leading to more efficient and secure communication systems.Conclusion:The future of quantum communication holds immense promise for secure and efficient communication systems. With advancements in quantum networks, the integration with classical communication, and the ultimate realization of a quantum internet, quantum communication will transform various industries. As researchers continue to overcome challenges and push the boundaries of technology, the potential applications for quantum communication are limitless. The next phase of communication is on the horizon,and it will be driven by the principles of quantum physics.。

Quantum MechanicsQuantum Mechanics is a fascinating and complex field of study that has revolutionized our understanding of the fundamental building blocks of the universe. It is a branch of physics that deals with the behavior of very small particles, such as atoms and subatomic particles, and how they interact with each other. The principles of quantum mechanics have led to the development of technologies such as lasers, transistors, and MRI machines, and have also had a profound impact on our understanding of the nature of reality. One of the key principles of quantum mechanics is the concept of superposition, which states that particles can exist in multiple states at the same time. This idea was famously illustrated by the thought experiment known as Schr?dinger's cat, in which a cat in a box is both alive and dead until the box is opened and the cat's state is observed. This idea challenges our everyday understanding of the world, where objects are either in one state or another, but it has been supported by numerous experimental observations. Another important concept in quantum mechanics is the idea of quantum entanglement, which Einstein famously referred to as "spooky action at a distance." This phenomenon occurs when two particles become linked in such a way that the state of one particle is instantly correlated with the state of the other, regardless of the distance between them. This idea has been demonstrated in experiments and has led to the development of technologies such as quantum cryptography, which promises to revolutionize the field of secure communication. However, despite the incredible success of quantum mechanics in explaining the behavior of particles at the smallest scales, it also presents significant challenges to our understanding of the nature of reality. For example, the famous double-slit experiment demonstrates that particles can behave as both waves and particles, depending on how they are observed. This has led to the development of various interpretations of quantum mechanics, such as the Copenhagen interpretation, the many-worlds interpretation, and the pilot-wave theory, each of which offers a different perspective on the nature of reality at the quantum level. Furthermore, the principles of quantum mechanics also have profound philosophical implications. For example, the idea that particles canexist in multiple states at the same time challenges our everyday understanding ofthe world and raises questions about the nature of consciousness and observation. Additionally, the concept of quantum entanglement raises questions about thenature of causality and the relationship between particles at a fundamental level. In conclusion, quantum mechanics is a field of study that has revolutionized our understanding of the fundamental building blocks of the universe. It has led tothe development of technologies that have transformed the modern world and hasalso raised profound questions about the nature of reality and the relationship between consciousness and the physical world. While it presents significant challenges to our understanding, it also offers incredible opportunities forfurther exploration and discovery. Overall, quantum mechanics is a field that continues to inspire and intrigue scientists and philosophers alike.。

Ultra-High Efficiency Photovoltaic Cells for Large Scale Solar Power GenerationYoshiaki NakanoAbstract The primary targets of our project are to dras-tically improve the photovoltaic conversion efficiency and to develop new energy storage and delivery technologies. Our approach to obtain an efficiency over40%starts from the improvement of III–V multi-junction solar cells by introducing a novel material for each cell realizing an ideal combination of bandgaps and lattice-matching.Further improvement incorporates quantum structures such as stacked quantum wells and quantum dots,which allow higher degree of freedom in the design of the bandgap and the lattice strain.Highly controlled arrangement of either quantum dots or quantum wells permits the coupling of the wavefunctions,and thus forms intermediate bands in the bandgap of a host material,which allows multiple photon absorption theoretically leading to a conversion efficiency exceeding50%.In addition to such improvements, microfabrication technology for the integrated high-effi-ciency cells and the development of novel material systems that realizes high efficiency and low cost at the same time are investigated.Keywords Multi-junctionÁQuantum wellÁConcentratorÁPhotovoltaicINTRODUCTIONLarge-scale photovoltaic(PV)power generation systems, that achieve an ultra-high efficiency of40%or higher under high concentration,are in the spotlight as a new technology to ease drastically the energy problems.Mul-tiple junction(or tandem)solar cells that use epitaxial crystals of III–V compound semiconductors take on the active role for photoelectric energy conversion in such PV power generation systems.Because these solar cells operate under a sunlight concentration of5009to10009, the cost of cells that use the epitaxial crystal does not pose much of a problem.In concentrator PV,the increased cost for a cell is compensated by less costly focusing optics. The photons shining down on earth from the sun have a wide range of energy distribution,from the visible region to the infrared region,as shown in Fig.1.Multi-junction solar cells,which are laminated with multilayers of p–n junctions configured by using materials with different band gaps,show promise in absorbing as much of these photons as possible,and converting the photon energy into elec-tricity with minimum loss to obtain high voltage.Among the various types of multi-junction solar cells,indium gallium phosphide(InGaP)/gallium arsenide(GaAs)/ger-manium(Ge)triple-junction cells that make full use of the relationship between band gaps and diverse lattice con-stants offered by compound semiconductors have the advantage of high conversion efficiency because of their high-quality single crystal with a uniform-size crystal lat-tice.So far,a conversion efficiency exceeding41%under conditions where sunlight is concentrated to an intensity of approximately5009has been reported.The tunnel junction with a function equivalent to elec-trodes is inserted between different materials.The positive holes accumulated in the p layer and the electrons in the adjacent n layer will be recombined and eliminated in the tunnel junction.Therefore,three p–n junctions consisting of InGaP,GaAs,and Ge will become connected in series. The upper limit of the electric current is set by the mini-mum value of photonflux absorbed by a single cell.On the other hand,the sum of voltages of three cells make up the voltage.As shown in Fig.1,photons that can be captured in the GaAs middle cell have a smallflux because of the band gap of each material.As a result,the electric currentoutputAMBIO2012,41(Supplement2):125–131 DOI10.1007/s13280-012-0267-4from the GaAs cell theoretically becomes smaller than that of the others and determines the electric current output of the entire tandem cell.To develop a higher efficiency tandem cell,it is necessary to use a material with a band gap narrower than that of GaAs for the middle cell.In order to obtain maximum conversion efficiency for triple-junction solar cells,it is essential to narrow down the middle cell band gap to 1.2eV and increase the short-circuit current density by 2mA/cm 2compared with that of the GaAs middle cell.When the material is replaced with a narrower band gap,the output voltage will drop.However,the effect of improving the electric current balance out-performs this drop in output voltage and boosts the effi-ciency of the entire multi-junction cell.When a crystal with such a narrow band gap is grown on a Ge base material,lattice relaxation will occur in the middle of epitaxial crystal growth because the lattice constants of narrower band-gap materials are larger than that of Ge (as shown in Fig.2).As a result,the carrier transport properties will degrade due to dislocation.Researchers from the international research center Solar Quest,the University of Tokyo,aim to move beyond such material-related restrictions,and obtain materials and structures that have effective narrow band gaps while maintaining lattice matching with Ge or GaAs.To achieve this goal,we have taken three approaches as indicated in Fig.3.These approaches are explained in detail below.DILUTE NITROGEN-ADDED BULK CRYSTAL Indium gallium nitride arsenide (InGaNAs)is a bulk material consists of InGaAs,which contains several percent of nitrogen.InGaNAs has a high potential for achieving a narrow band gap while maintaining lattice matching with Ge or GaAs.However,InGaNAs has a fatal problem,that is,a drop in carrier mobility due to inhomogeneousdistribution of nitrogen (N).To achieve homogeneous solid solution of N in crystal,we have applied atomic hydrogen irradiation in the film formation process and addition of a very small amount of antimony (Sb)(Fig.3).The atomic hydrogen irradiation technology and the nitrogen radical irradiation technology for incorporating N efficiently into the crystal can be achieved only through molecular beam epitaxy (MBE),which is used to fabricate films under high vacuum conditions.(Nitrogen radical irradiation is a technology that irradiates the surface of a growing crystal with nitrogen atoms that are resolved by passing nitrogen through a plasma device attached to the MBE system.)Therefore,high-quality InGaNAs has been obtained only by MBE until now.Furthermore,as a small amount of Sb is also incorporated in a crystal,it is nec-essary to control the composition of five elements in the crystal with a high degree of accuracy to achieve lattice matching with Ge or GaAs.We have overcome this difficulty by optimizing the crystal growth conditions with high precision and devel-oped a cell that has an InGaNAs absorption layer formed on a GaAs substrate.The short-circuit current has increased by 9.6mA/cm 2for this cell,compared with a GaAs single-junction cell,by narrowing the band gap down to 1.0eV.This technology can be implemented not only for triple-junction cells,but also for higher efficiency lattice-matched quadruple-junction cells on a Ge substrate.In order to avoid the difficulty of adjusting the compo-sition of five elements in a crystal,we are also taking an approach of using GaNAs with a lattice smaller than that of Ge or GaAs for the absorption layer and inserting InAs with a large lattice in dot form to compensate for the crystal’s tensile strain.To make a solid solution of N uniformly in GaNAs,we use the MBE method for crystal growth and the atomic hydrogen irradiation as in the case of InGaNAs.We also believe that using 3D-shaped InAs dots can effectively compensate for the tensile strainthatFig.1Solar spectrum radiated on earth and photon flux collected by the top cell (InGaP),middle cell (GaAs),and bottom cell (Ge)(equivalent to the area of the filled portions in the figure)occurs in GaNAs.We have measured the characteristics of a single-junction cell formed on a GaAs substrate by using a GaNAs absorption layer with InAs dots inserted.Figure 4shows that we were able to succeed in enhancing the external quantum efficiency in the long-wavelength region (corresponding to the GaNAs absorp-tion)to a level equal to GaAs.This was done by extending the absorption edge to a longer wavelength of 1200nm,and increasing the thickness of the GaNAs layer by increasing the number of laminated InAs quantum dot layers.This high quantum efficiency clearly indicates that GaNAs with InAs dots inserted has the satisfactory quality for middle cell material (Oshima et al.2010).STRAIN-COMPENSATED QUANTUM WELL STRUCTUREIt is extremely difficult to develop a narrow band-gap material that can maintain lattice matching with Ge orGaAs unless dilute nitrogen-based materials mentioned earlier are used.As shown in Fig.2,the conventionally used material InGaAs has a narrower band gap and a larger lattice constant than GaAs.Therefore,it is difficult to grow InGaAs with a thickness larger than the critical film thickness on GaAs without causing lattice relaxation.However,the total film thickness of InGaAs can be increased as an InGaAs/GaAsP strain-compensated multi-layer structure by laminating InGaAs with a thickness less than the critical film thickness in combination with GaAsP that is based on GaAs as well,but has a small lattice constant,and bringing the average strain close to zero (Fig.3.).This InGaAs/GaAsP strain-compensated multilayer structure will form a quantum well-type potential as shown in Fig.5.The narrow band-gap InGaAs layer absorbs the long-wavelength photons to generate electron–hole pairs.When these electron–hole pairs go over the potential bar-rier of the GaAsP layer due to thermal excitation,the electrons and holes are separated by a built-in electricfieldFig.2Relationship between band gaps and lattice constants of III–V-based and IV-based crystalsto generate photocurrent.There is a high probability of recombination of electron–hole pairs that remain in the well.To avoid this recombination,it is necessary to take out the electron–hole pairs efficiently from the well and transfer them to n-type and p-type regions without allowing them to be recaptured into the well.Designing thequantumFig.3Materials and structures of narrow band-gap middle cells being researched by thisteamFig.4Spectral quantum efficiency of GaAs single-junction cell using GaNAs bulk crystal layer (inserted with InAs dots)as the absorption layer:Since the InAs dot layer and the GaNAs bulk layer are stacked alternately,the total thickness of GaNAs layers increases as the number of stacked InAs dot layers is increased.The solid line in the graph indicates the data of a reference cell that uses GaAs for its absorption layer (Oshima et al.2010)well structure suited for this purpose is essential for improving conversion efficiency.The high-quality crystal growth by means of the metal-organic vapor phase epitaxy (MOVPE)method with excellent ability for mass production has already been applied for InGaAs and GaAsP layers in semiconductor optical device applications.Therefore,it is technologically quite possible to incorporate the InGaAs/GaAsP quantum well structure into multi-junction solar cells that are man-ufactured at present,only if highly accurate strain com-pensation can be achieved.As the most basic approach related to quantum well structure design,we are working on fabrication of super-lattice cells with the aim of achieving higher efficiency by making the GaAsP barrier layer as thin as possible,and enabling carriers to move among wells by means of the tunnel effect.Figure 6shows the spectral quantum effi-ciency of a superlattice cell.In this example,the thickness of the GaAsP barrier layer is 5nm,which is not thin enough for proper demonstration of the tunnel effect.When the quantum efficiency in the wavelength range (860–960nm)that corresponds to absorption of the quan-tum well is compared between a cell,which has a con-ventionally used barrier layer and a thickness of 10nm or more,and a superlattice cell,which has the same total layer thickness of InGaAs,the superlattice cell demonstrates double or higher quantum efficiency.This result indicates that carrier mobility across quantum wells is promoted by even the partial use of the tunnel effect.By increasing the P composition in the GaAsP layer,the thickness of well (or the In composition)can be increased,and the barrier layer thickness can be reduced while strain compensation is maintained.A cell with higher quantum efficiency can befabricated while extending the absorption edge to the long-wavelength side (Wang et al.2010,2012).GROWTH TECHNIQUE FOR STRAIN-COMPENSATED QUANTUM WELLTo reduce the strain accumulated in the InGaAs/GaAsP multilayer structure as close to zero as possible,it is nec-essary to control the thickness and atomic content of each layer with high accuracy.The In composition and thickness of the InGaAs layer has a direct effect on the absorption edge wavelength and the GaAsP layer must be thinned to a satisfactory extent to demonstrate fully the tunnel effect of the barrier layer.Therefore,it is desirable that the average strain of the entire structure is adjusted mainly by the P composition of the GaAsP layer.Meanwhile,for MOVPE,there exists a nonlinear rela-tionship between the P composition of the crystal layer and the P ratio [P/(P ?As)]in the vapor phase precursors,which arises from different absorption and desorption phenomena on the surface.As a result,it is not easy to control the P composition of the crystal layer.To break through such a difficulty and promote efficient optimiza-tion of crystal growth conditions,we have applied a mechanism to evaluate the strain of the crystal layer during growth in real time by sequentially measuring the curvature of wafers during growth with an incident laser beam from the observation window of the reactor.As shown in Fig.7,the wafer curvature during the growth of an InGaAs/GaAsP multilayer structure indicates a periodic behavior.Based on a simple mechanical model,it has become clear that the time changes ofwaferFig.5Distribution of potential formed by the InGaAs/GaAsP strain-compensated multilayer structure:the narrow band-gap InGaAs layer is sandwiched between wide band-gap GaAsP layers and,as a result,it as quantum well-type potential distribution.In the well,electron–hole pairs are formed by absorption of long-wavelength photons and at the same time,recombination of electrons and holes takes place.The team from Solar Quest is focusing on developing a superlattice structure with the thinnest GaAsP barrier layercurvature are proportionate to the strain of the crystal layer relative to a substrate during the growing process.One vibration cycle of the curvature is same as the growth time of an InGaAs and GaAsP pair (Sugiyama et al.2011).Therefore,the observed vibration of the wafer curvature reflects the accumulation of the compression strain that occurs during InGaAs growth and the release of the strain that occurs during GaAsP growth.When the strain is completely compensated,the growth of the InGaAs/GaAsP pair will cause this strain to return to the initial value and the wafer curvature will vibrate with the horizontal line as the center.As shown in Fig.7,strain can be compensated almost completely by adjusting the layer structure.Only by conducting a limited number of test runs,the use of such real-time observation technology of the growth layer enables setting the growth conditions for fabricating the layer structure for which strain has been compensated with highaccuracy.Fig.6Spectral quantum efficiency of GaAs single-junction cell using InGaAs/GaAsP superlattice as theabsorption layer:This structure consists of 60layers of InGaAs quantum wells.The graph also shows data of a reference cell that uses GaAs for its absorption layer (Wang et al.2010,2012)Fig.7Changes in wafer curvature over time during growth of the InGaAs/GaAsP multilayer structure.This graph indicates the measurement result and the simulation result of the curvature based on the layer structure(composition ?thickness)obtained by X-ray diffraction.Since compressive strain is applied during InGaAs growth,the curvature decreases as time passes.On the other hand,since tensile strain is applied during GaAsP growth,the curvature changes in the oppositedirection (Sugiyama et al.2011)FUTURE DIRECTIONSIn order to improve the conversion efficiency by enhancing the current matching of multi-junction solar cells using III–V compound semiconductors,there is an urgent need to create semiconductor materials or structures that can maintain lattice matching with Ge or GaAs,and have a band gap of1.2eV.As for InGaNAs,which consists of InGaAs with several percent of nitrogen added,we have the prospect of extending the band edge to1.0eV while retaining sufficient carrier mobility for solar cells by means of atomic hydrogen irradiation and application of a small quantity of Sb during the growth process.In addition,as for GaNAs bulk crystal containing InAs dots,we were able to extend the band edge to1.2eV and produce a high-quality crystal with enoughfilm thickness to achieve the quantum efficiency equivalent to that of GaAs.These crystals are grown by means of MBE. Therefore,measures that can be used to apply these crys-tals for mass production,such as migration to MOVPE, will be investigated after demonstrating their high effi-ciency by embedding these crystals into multi-junction cells.As for the InGaAs/GaAsP strain-compensated quantum well that can be grown using MOVPE,we are working on the development of a thinner barrier layer while compen-sating for the strain with high accuracy by real-time observation of the wafer curvature.We have had the prospect of achieving a quantum efficiency that will sur-pass existing quantum well solar cells by promoting the carrier transfer within the multilayer quantum well struc-ture using the tunnel effect.As this technology can be transferred quite easily to the existing multi-junction solar cell fabrication process,we strongly believe that this technology can significantly contribute to the efficiency improvement of the latest multi-junction solar cells. REFERENCESOshima,R.,A.Takata,Y.Shoji,K.Akahane,and Y.Okada.2010.InAs/GaNAs strain-compensated quantum dots stacked up to50 layers for use in high-efficiency solar cell.Physica E42: 2757–2760.Sugiyama,M.,K.Sugita,Y.Wang,and Y.Nakano.2011.In situ curvature monitoring for metalorganic vapor phase epitaxy of strain-balanced stacks of InGaAs/GaAsP multiple quantum wells.Journal of Crystal Growth315:1–4.Wang,Y.,Y.Wen,K.Watanabe,M.Sugiyama,and Y.Nakano.2010.InGaAs/GaAsP strain-compensated superlattice solar cell for enhanced spectral response.In Proceedings35th IEEE photovoltaic specialists conference,3383–3385.Wang,Y.P.,S.Ma,M.Sugiyama,and Y.Nakano.2012.Management of highly-strained heterointerface in InGaAs/GaAsP strain-balanced superlattice for photovoltaic application.Journal of Crystal Growth.doi:10.1016/j.jcrysgro.2011.12.049. AUTHOR BIOGRAPHYYoshiaki Nakano(&)is Professor and Director General of Research Center for Advanced Science and Technology,the University of Tokyo.His research interests include physics and fabrication tech-nologies of semiconductor distributed feedback lasers,semiconductor optical modulators/switches,monolithically integrated photonic cir-cuits,and high-efficiency heterostructure solar cells.Address:Research Center for Advanced Science and Technology, The University of Tokyo,4-6-1Komaba,Meguro-ku,Tokyo153-8904,Japan.e-mail:nakano@rcast.u-tokyo.ac.jp。

Absolutely Maximally Entangled States:Existence and ApplicationsWolfram Helwig and Wei CuiCenter for Quantum Information and Quantum Control (CQIQC),Department of Physics,University of Toronto,Toronto,Ontario,M5S 1A7,CanadaJune 12,2013AbstractWe investigate absolutely maximally entangled (AME)states,which are multipartite quantum states that are maximally entangled with re-spect to any possible bipartition.These strong entanglement properties make them a powerful resource for a variety of quantum information pro-tocols.In this paper,we show the existence of AME states for any number of parties,given that the dimension of the involved systems is chosen ap-propriately.We prove the equivalence of AME states shared between an even number of parties and pure state threshold quantum secret sharing (QSS)schemes,and prove necessary and sufficient entanglement proper-ties for a wider class of ramp QSS schemes.We further show how AME states can be used as a valuable resource for open-destination teleporta-tion protocols and to what extend entanglement swapping generalizes to AME states.1IntroductionEntanglement has been a hot topic since the beginning of quantum mechanics and fueled a lot of discussions,among them most notable the Einstein-Podolsky-Rosen (EPR)paradox [1],which finally led Bell to come up with a method of actually measuring entanglement [2].It was not until the advent of quantum information,however,that entanglement was recognized as a useful resource.Almost all applications in quantum information make either explicit or implicit use of entanglement,which makes it crucial to gain as much insight as possible.[3]While the entanglement of bipartite states is already very well understood[4,5,6],the road to its generalization to more than two parties is paved with many obstacles.Therefore we often have to restrict ourselves to special cases when analyzing multipartite entanglement.A prominent choice are states that extremize the entanglement for a certain measure of entanglement.In this paper we want to do that by focusing on absolutely maximally entangled (AME)states,which are defined as states that are maximally entangled for any possible bipartition.[7,8,9]1a r X i v :1306.2536v 1 [q u a n t -p h ] 11 J u n 2013Definition1.An absolutely maximally entangled state is a pure state,shared among n parties P={1,...,n},each having a system of dimension d.Hence |Φ ∈H1⊗···⊗H n,where H i∼=C d,with the following equivalent properties: (i)|Φ is maximally entangled for any possible bipartition.This means thatfor any bipartition of P into disjoint sets A and B with A∪B=P and, without loss of generality,m=|B|≤|A|=n−m,the state|Φ can be written in the form|Φ =1√d mk∈Z md|k1 B1···|k m B m|φ(k) A,(1)with φ(k)|φ(k ) =δkk .(ii)The reduced density matrix of every subset of parties A⊂P with|A|= n2 is totally mixed,ρA=d− n2 1d n2.(iii)The reduced density matrix of every subset of parties A⊂P with|A|≤n2 is totally mixed.(iv)The von Neumann entropy of every subset of parties A⊂P with|A|= n2 is maximal,S(A)= n2 log d.(v)The von Neumann entropy of every subset of parties A⊂P with|A|≤n2 is maximal,S(A)=|A|log d.These are all necessary and sufficient condition for a state to be absolutely max-imally entangled.We denote such a state as an AME(n,d)state.The simplest examples of AME states occur for low dimensional systems shared among few parties.Starting with qubits,the most obvious one is an EPR pair,which is maximally entangled for its only possible bipartition.For three qubits shared among three parties,we can recognize the GHZ state as an AME state.It is maximally entangled,with1ebit of entanglement with respect to every bipartition.For four qubits,there is no obvious candidate,and in fact it has been shown that for four qubits no AME state exists[9].We can stillfind an absolutely maximally entangled states for four parties,however,by increasing the dimensions of the involved systems.An AME(4,3)state for four qutrits shared among four parties exists,and it is given by[7]|Φ =1√92i,j=0|i |j |i+j |i+2j .(2)This is thefirst indicator that the search for AME states gets more promising as we increase the dimensions of the systems.Completing the characterization of AME states for qubits,it is known that AME states exist for5and6qubits.Explicit forms for them are given in Ref.[7], and it turns out that they are closely related to thefive-qubit error correction code.For7qubits,it is still not known if an AME state exists,whereas for≥8 qubits,it has been shown that no AME states can exist[9,10].In Ref.[7],we showed how AME states can be used for parallel teleportation protocols.In these protocols,the parties are divided into a sets of senders2and receivers,respectively.One of the two sets is given the ability to perform joint quantum operations,while players in the other set can only perform local quantum operations.Under these conditions,a parallel teleportation of multiple quantum states is possible if the set that performs joint quantum operations is larger than the other set.A closer look at these teleportation scenarios then led to the observation that any AME state shared by an even number of parties can be used to construct a threshold quantum secret sharing(QSS)scheme[11, 12,13].The opposite direction was also shown,with one additional condition imposed on the QSS scheme,namely that the shared state that encodes the secret is already an AME state.In this paper,we will give an information-information theoretic proof of this equivalence of AME states and threshold QSS scheme,which shows that the additional condition is not required.We will rather see that it is satisfied for all threshold QSS schemes.We will further give a recipe of how to construct AME states from classical codes that satisfy the Singleton bound[14].This construc-tion can be used to produce AME states for a wide class of parameters,and it even proves that AME states exist for any number of parties for appropriate system dimension.A result that could also be deduced from the equivalence of AME states and QSS schemes and a known construction for threshold QSS schemes[11].We will then show more applications for AME states.Thefirst be-ing the construction of a wider class of QSS schemes,the ramp QSS schemes,of which threshold QSS schemes are a special case.The next one is the utilization of AME states as resources for open-destination teleportation protocols[15]. Finally,we investigate to what extend entanglement can be swapped between two AME states.This paper is structured as follows.In Section2,we show how AME states can be constructed from classical codes,which also also shows the existence of AME states for any number of parties.In Section3,we establish an equiv-alence between even party AME states and threshold QSS schemes,using an information theoretic approach to QSS schemes.Section4shows how to share multiple secrets using AME states.In Section5,we show that AME states can be used for open-destination teleportation.After that,swapping of AME states is investigated in Section6.2Constructing AME States from Classical MDS CodesThere is a subclass of AME(n,d)states that can be constructed from optimal classical error correction codes.A classical code C consists of M codewords of length n over an alphabetΣof size d.For our purposes,the alphabet isgoing to beΣ=Z d and thus C⊂Z nd .The Hamming distance between twocodewords is defined as the number of positions in which they differ,and the minimal distanceδof the code C as the minimal Hamming distance between any two codewords.For a given length n and minimal distanceδ,the number of codewords M in the code is bounded by the Singleton bound[14,16]M≤d n−δ+1.(3) Codes that satisfy the Singleton bound are referred to as maximum-distance separable(MDS)codes.They can be used to construct AME states:3Theorem2(a).From a classical MDS code C⊂Z2md of length2m and minimaldistanceδ=m+1over an alphabet Z d,an AME(2m,d)state can be constructed as|AME =1√d mc∈C|c (4)=1√d mc∈C|c1 1···|c m m|c m+1 m+1···|c2m 2m.(5)Proof.The code C satisfies the Singleton bound,which means the sum contains a total of M=d2m−δ+1=d m terms.Furthermore,any two of these terms differ in at least one of thefirst m kets because the code has minimal distance δ=m+1.Hence the sum contains each possible combination of thefirst m basis kets exactly once.Moreover,for any two different terms,the last m kets must also differ in at least one ket and are thus orthogonal.This means the state has the form of Equation(1)with respect to the bipartition into thefirst m and last m parties.The same argument works for any other bipartition into two sets of size m,hence the state is absolutely maximally entangled.An analogous argument shows that a similar construction for an odd number of parties results in an AME state.Theorem2(b).From a classical MDS code C⊂Z2m+1d of length2m+1andminimal distanceδ=m+2over an alphabet Z d,an AME(2m+1,d)state can be constructed as|AME =1√d mc∈C|c (6)=1√d mc∈C|c1 1···|c m+1 m+1|c m+2 m+2···|c2m 2m+1.(7)Proof.The code contains M=d m terms.Each of the terms differ in at least one of thefirst m+1and last m terms.Thus,with the same argument as above, this is an AME state.Trivial states of that form are d-dimensional EPR states,which are repre-sented by the code with codewords00,11,...,(d−1)(d−1).This code has n=2,δ=2,M=d1.For n=3,we canfind the GHZ states for arbitrary dimensions, which can be constructed from the code000,111,...,(d−1)(d−1)(d−1),which hasδ=3and M=d1.As already mentioned in the introduction,for n=4 no AME state exists for d=2,however for d=3the AME(4,3)state given in Equation(2)can also be constructed from an MDS code,the[4,2,3]3ternary Hamming code.A wide class of MDS codes is given by the Reed-Solomon codes and its generalizations[17,16,18],which give MDS codes for n=d−1,n=d,and n=d+1,for d=p x being a positive power of a prime number p.From the Reed-Solomon codes,MDS codes can also be constructed for n<d−1[14].This shows that AME states exist for any number of parties if the system dimensions are chosen right.At this point we would like to mention that after posting a preliminary ver-sion of our last paper on this subject[7],it has been brought to our attention by4Gerardo Adesso that the results of this section have already been previously dis-covered by Ashish Thapliyal and coworkers,and were presented at a conference in 2003[19],but remained unpublished.3Equivalence of AME states and QSS schemes In Ref.[7],we showed that AME(2m,d )states,i.e.,AME states shared between an even number of parties,are equivalent to pure state threshold quantum secret sharing (QSS)schemes that have AME states as basis states and share and secret dimension equal to d .Here we will give an information-theoretic proof of this equivalence,which shows that the requirement that the basis states of the QSS scheme are AME states is redundant,as it follows from this proof that these states are always absolutely maximally entangled.Before stating the theorem and the proof,we give a short motivation why AME states and QSS schemes are related.Consider an AME(2m,d )state shared among an even number of parties.If we take any bipartition into two sets of parties A and B ,each of size m ,a d m dimensional state can be teleported from one set to the other due to the maximal entanglement between A and B .Moreover,we have shown in Ref.[7],that the teleportation can be performed in such a way that each party in the sending set B performs a local teleportation operation on their qudit,while the parties in the receiving set A perform a joint quantum operation to recover all m teleported qudits.This is depicted in Figure 1for the case of m =4.This also works if only one party in B ,which we call the dealer D ,performs the teleportation operation,while the others do nothing.Then the teleported d -dimensional state can still be recovered by the players in set A .Furthermore,this also works for any other bipartition into sets A and B of size m ,with D ∈B ,without changing the teleportation operation D has to perform,but now the parties in A can recover the teleported state (see Figure 2).This means that any set with m parties can recover the state.Moreover,the no-cloning theorem guarantees that the complement of a set that can recover the state has no information about the state.Hence all sets with less than m parties cannot gain any information about the state.This,however,are exactly the requirements for a threshold QSS scheme,therefore we have constructed a ((m,2m −1))threshold QSS scheme from the AME(2m,d )state.To formally show this,and moreover that it also works in the opposite direction,meaning that a ((m,2m −1))threshold QSS scheme is always related to an AME(2m,d )state,we will use the information theoretic description of QSS schemes as introduced in Ref.[13].Let us quickly review the framework for a pure state ((m,2m −1))threshold QSS scheme [11].A secret S is distributed among the players P ={1,...,2m −1}such that any set A ⊆P with |A |≥m can recover the secret,while any set B ⊂P with |B |<m cannot gain any information about the secret.We further only consider the case where the dimension d of the secret is the same as the dimension of each player’s share.The secret is assumed to lie in the Hilbert space H S ∼=C d ,and the share of party i in H i ∼=C d .The encoding is described by an isometryU S :H S →H 1⊗···⊗H 2m −1.(8)The secret S is chosen randomly and thus is described by ρS =1/di |i i |.We5Figure 1:(Color online)Parties in B (green)perform local teleportation op-erations,parties in A (red)can recover teleported states by performing a joint quantumoperationFigure 2:(Color online)After D (blue)performs her teleportation operation,any set of m parties (red),A ,A ,A etc.,can recover the teleported state.Any set of parties with m −1or less parties (any set consisting only of green parties)cannot gain any information about the teleported state.consider its purification by introducing a reference system R such that |RS =1/√d i |i |i ∈H R ⊗H S .Let ρRA denote the combined state of the reference system and a set of players A ⊆P after U S has been applied to the secret.Then the players A can recover the secret,if there exists a completely positive map T A :H A →H S such that [13,20]1R ⊗T A (ρRA )=|RS .(9)This can be stated in terms of the mutual informationI (X :Y )=S (X )+S (Y )−S (X,Y )(10)as follows:Definition 3.An isometry U S :H S →H 1⊗···⊗H 2m −1creates a ((m,2m −1))threshold QSS scheme if and only if,after applying to the system S of the pu-rification |RS ,the mutual information between R and an authorized (unautho-rized)set of players A (B )satisfiesI (R :A )=I (R :S )=2S (S )if |A |≥m (11)I (R :B )=0if |B |<m.(12)6Here S is the von Neumann entropy,and because of S(i)≥S(S)[13],we haveS(S)=S(R)=S(i)=log d.(13) From Equations(10)to(12)it immediately follows thatS(R,A)=S(A)−S(R)if|A|≥m(14)S(R,B)=S(B)+S(R)if|B|<m.(15)Theorem4.For a state|Φ the following two properties are equivalent:(i)|Φ is an AME(2m,d)state.(ii)|Φ is the purification of a((m,2m−1))threshold QSS scheme,whose share and secret dimensions are d.Proof.(i)→(ii):We need to show that for an AME(2m,d)state Equations(11) and(12)are satisfied,where R can be any of the2m party.This follows directly from the definition of the mutual information,Equation(10),and Defintion1 (v).(ii)→(i):Consider an unauthorized set of players B,with|B|=m−1. Then the set is B∪i is authorized for any additional player i/∈B,and from Equation(14)we haveS(B,i,R)=S(B,i)−S(R)(16)On the other hand,using the Araki-Lieb inequality[21]S(X,Y)≥S(X)−S(Y) and Equation(15)givesS(B,i,R)≥S(B,R)−S(i)=S(B)+S(R)−S(i).(17)Combining the last two equations and using S(S)=S(R)=S(i)showsS(B,i)≥S(B)+S(i),(18)where equallity must hold due to the subadditivity of the entropy S(X,Y)≤S(X)+S(Y).This means that the entropy increases maximally when adding one player’s share to m−1shares.The strong subadditivity of the entropy[21]S(X,Y)−S(Y)≥S(X,Y,Z)−S(Y,Z)(19)states that adding one system X to a system Y increases the entropy at least by as much as adding the system X to a larger system Y∪Z that contains Y. So in our case,adding one share to less than m−1shares increases the entropy by at least S(i),and since this is the maximum,it increases the entropy exactly by S(i).Hence,starting out with a set of no shares,and repeatedly adding one share to the set until the set contains any m shares and is authorized,shows that any set of m shares has entropy mS(i).This shows that the entropy is maximal for any subset of m parties and thus|Φ is an AME(2m,d)state.Corollary5.The encoded state U S|S of a specific secret|S with a((m,2m−1))threshold QSS protocol with share and secret dimension d is an AME(2m−1,d)state.74Sharing multiple secretsIn the previous section,we outlined how an AME state can be used to construct a QSS scheme.The role of the dealer is assigned to one of the parties and he performs a teleportation operation on his qudit,which encodes the teleported qudit onto the qudits of the remaining parties such that the criteria for a QSS scheme are met.While Theorem 4shows the equivalence of AME states and QSS schemes,the actual protocol for the encoding and decoding operations has been presented in Ref.[7].Note that in the described scenario,the role of the dealer can be assigned to any player.Thus one may ask,what happens if more than one of the players assumes the role of the dealer.The answer is that,given an AME(2m,d )state,up to m players are able to independently encode one qudit each onto the qudits of the remaining players in such a way that results in a QSS scheme with a more general access structure.For a secret sharing scheme with a general access structure,each set of players falls into one of three categories [22,23].1.Authorized :A set of players is authorized,if it can recover the secret2.Forbidden :A set of players is called a forbidden set,if the players cannot gain any information about the encoded secret3.Intermediate :A set of players is classified as an intermediate set,if they cannot recover set secret,but may be able to gain part of the information.This means that the reduced density matrix of that set of players depends on the encoded secret,but not enough as to recover the secret.A special kind of access structure is a (m,L,n )ramp secret sharing scheme[24].Here n is the total number of players,m is the number of players needed to recover the secret,and L is the number of shares that have to be removed from a minimal authorized set to destroy all information about the secret.In terms of the above defined set categories that means that any set of m or more players is authorized,any set of m −L or less players is forbidden,and any set consisting of more than m −L ,but less than m players is an intermediate set.This is the access structure we get from an AME(2m,d )state if more than one party assumes the role of the dealer.Theorem 6.Given an AME(2m,d )state,a QSS scheme with secret dimension d L and a (m,L,2m −L )ramp access structure can be constructed for all 1≤L ≤m .Proof.The encoding of the secret is done by assigning the role of dealer to L of the 2m players.For simplicity we choose them to be the first L players.Each of them performs a Bell measurement on their respective qudit of the AME state and one qudit of the secret.The Bell measurement is described by the general d -dim Bell states |Ψkl and the unitaries U kl that transform among them [25]|Ψqp =1√d j e 2πijq/d |j |j +p (20)U qp = j e 2πijq/d |j j +p |,(21)8where the kets are understood to be mod d .For a secret |s and outcomes (q 1,p 1)...(q L ,p L )for the Bell measurement of the dealers,the initial AME(2m,d )state is transformed to|ΦS =1√ k ∈Z m ds qp ,k 1···k L |k L +1 B 1···|k m B m −L |φ(k ) A .(22)Heres qp ,k 1···k L = k 1···k L |U †q 1p 1⊗···⊗U †q L p L |s ,(23)and the partition of the remaining 2m −L parties into two sets A and B of size m and m −L ,respectively,is arbitrary.After obtaining their measurement outcomes,the dealers broadcast their results to all of the remaining players.This concludes the encoding process.To show that any set of m or more players is authorized,it suffices to show that set A in Equation22can recover the secret.They can do so by applying the unitary operationU =(U q 1p 1⊗···⊗U q L p L ⊗1)V(24)withV =k ∈Z m d |k 1 ···|k m φ(k )|,(25)to their system.This changes the state toU |ΦS =1√d m −L (k L +1,...,k m )∈Z m −L d |k L +1 B 1···|k m B m −L |s A |k L +1 A L +1···|k m A m (26)where A ={A 1,...,A L }.Thus the players in set A have the secret in their possession.It immediately follows from the no-cloning theorem that B ,and thus any set of size m −L or less,cannot have any information about the secret since all information is located in the complement set.Alternatively,this also follows from the observation that the reduced density matrix of B is always completely mixed,independent of the secret.The last thing left to show is that all sets with more than m −L but fewer than m players are indeed intermediate sets.To see that,consider the case L =1,where a set C of m −1players is not authorized to recover the secret.If one more player in the complement of C assumes the role of the dealer,the scheme is changes to L =2.This operation does not change the fact that C cannot recover the first secret,and thus it is still not authorized for L =2.This argument can be continued to any other 1<L ≤m by adding more dealers.Hence a set of m −1(or fewer)players is not authorized to recover the secret for all value of 1≤L ≤m .That a set of more than m −L players is not forbidden follows from the fact that information cannot be lost and thus the complement of a forbidden set has to be authorized.However,we just argued that the complement of a set of more than m −L players is not authorized (since it consists of less than m players).Hence any set with more than m −L and fewer than m players is an intermediate set.9A closer look at the proof shows us that it actually is not absolutely necessary for the initial state to be maximally entangled with respect to any bipartition,but only for bipartitions for which all dealers are in the same set.In fact,we can generalize the proof of Theorem 4to the case of ramp QSS to show that this is a necessary and sufficient condition for the construction of (m,L,2m −L )ramp QSS schemes.Theorem 7.For a state |Φ ∈H P ⊗H R ,shared between 2m −L players P ,each holding a qudit,and L reference qudits,the following two properties are equivalent:(i)|Φ is maximally entangled for any bipartition for which the L referencequdits are in the same set.(ii)|Φ is the purification of a (m,L,2m −L )ramp QSS schemes.The encodedsecret of the ramp QSS scheme has dimension d L ,and each share has dimension d .The proof is a straightforward generalization of the proof of Theorem 4and is provided in Appendix A.5Open-destination teleportationGiven a state with such high amount of entanglement as the AME state has,one cannot help thinking about ways of using these resources for teleportation protocols.In Ref.[7]we already showed how AME states can be used for two different teleportation scenarios that require either sending or receiving parties to perform joint quantum operations,while the other end may only use local quantum operations.Another teleportation scenario that uses genuine multipartite entanglement,and has already been demonstrated experimentally [15],is open-destination tele-portation.In this scenario,a genuinely multipartite entangled state is shared between n parties,each in the possession of one qudit.One of the parties,the dealer,performs a teleportation operation on her qudit and an ancillary qudit |Φ .After this teleportation operation,the final destination of |Φ is still un-decided,thus open-destination teleportation.The destination is decided upon in the next step,where a subset A of the remaining parties P performs a joint quantum operation on their qudits such that a player in P \A ends up with the state |Φ –up to local operations that depend on measurement outcomes of the dealer and parties A .Here we want to show that open-destination teleportation can also be performed with AME states.Assume that an AME(n,d )state has been distributed among n parties.One of the n parties is assigned the role of the dealer.She performs a Bell measurement on her qudit and the secret |S = a i |i .This transforms the state to|S |Φ →|ΦS =1√d m (k,i )∈Z m da pq,i |k 1 B 1···|k m −1 B m −1|φ(k,i ) A ,(27)where pq labels the outcome of the Bell measurement and has to be made public.The remaining n −1parties that share the resulting state have been divided10into two sets A and B of size n/2 and m−1= n/2 −1,respectively.Now,after the teleportation operation has been completed,the parties in set Amay choose one party B i∈B as thefinal destination for the state|S .Then, after performing the joint unitary operation of Equation(25)followed by a Bellmeasurement on qudits A i and A m with outcome rs,the party B i ends up withthe state|ΦB i =U†rs U†pq|S ,which can be easily transformed to|S if themeasurement results pq and rs are known.Note that with the parallel teleportation protocol introduced in Ref.[7],also one of the parties in A can be chosen to receive the state|S .Thus,after the dealer’s teleportation operation is completed,any set of size greater or equal n/2 can choose any of the remaining n−1parties as thefinal destination of the teleportation.116Swapping of AME statesEntanglement swapping [26]is a very useful tool for the application of entan-glement in communication.By making a Bell measurement on Bob’s side,two entangled states shared between Alice and Bob,and Bob and Charlie,respec-tively,can be transformed into an entangled state shared by Alice and Charlie.Employing this procedure in quantum repeaters [27]allows entangled states to be used for long distance communications.In this section,we show to what ex-tent a generalization of the entanglement swapping protocol can be constructed to allow swapping of entanglement between absolutely maximally entangled states shared between different parties.Assume that parties {1,2,...,2n }share an AME(2n,d )state,|Φ 1,...,2n = |i 1···i n 1,...,n |φ(i 1,...,i n ) n +1,...,2n (28)= |i 1···i n 1,...,n U |i 1···i n n +1,...,2n ,(29)where U is a unitary transformation with U |i 1···i n =|φ(i 1,...,i n ) .Suppose parties {n +1,...,3n }also share an AME(2n,d )state|Φ n +1,...,3n = |i 1···i n n +1,...,2n U |i 1···i n 2n +1,...,3n .(30)Now each of the parties {n +1,...,2n }performs a Bell measurement on their qudits from both AME states.Without loss of generality,we can assume the measurement result is (q,p )=(0,0)(see Equation (20)for the notation),since other measurement outcomes produce the same state up to local transforma-tions.Then the state shared by the parties {1,...,n,2n +1,...,3n }becomes|Φ 1,...,n,2n +1,...,3n = |i 1···i n 1,...,n U 2|i 1···i n 2n +1,...,3n (31)Consecutive applications of the above procedure gives the following lemma:Lemma 8.Suppose each group of parties {1,...,2n },{n +1,...,3n },···,{mn +1,...,(m +1)n }shares an AME(2n,d )state,|Φ = |i 1···i n U |i 1···i n .(32)Then,if each of the parties {n +1,n +2,...,mn }performs a Bell measurement on their two qudits,the resulting state shared by the parties {1,...,n,mn +1,...,(m +1)n }is locally equivalent to|Φ 1,...,n,mn +1,...,(m +1)n = |i 1···i n 1,...,n U m |i 1···i n mn +1,...,(m +1)n (33)Proof by induction.The case for m =2is demonstrated in the above discussion already.If the lemma holds for m ,for m +1the two remaining states,after the parties {n +1,n +2,...,mn }performed their Bell measurements,are |Φ 1,...,n,mn +1,...,(m +1)n = |i 1···i n 1,...,n U m |i 1···i n mn +1,...,(m +1)n (34)12。

全空间无人体系管控中心通用技术要求英文1. IntroductionThe development of unmanned control centers for all-territory space is an important aspect of modern technology. In order to ensure the smooth operation and safety of these control centers, it is crucial to establish universal technical requirements that can be applied across different spaces and environments. This document 本人ms to outline the general technical requirements for unmanned control centers in all-territory spaces in English.2. System Architecture2.1. The unmanned control center should have a modular and scalable architecture that can be adapted to different space environments and requirements.2.2. The system should be capable of real-time data processing, analysis, and decision-making.2.3. The architecture should be designed to facilitate seamlessmunication and integration with other systems and devices.3. Communication3.1. The control center should have reliable andsecuremunication capabilities, including both terrestrial and satellitemunication.3.2. The system should be able to handle a large volume of data transmission and ensure low-latencymunication.3.3. Themunication network should be resistant to interference and capable of operating in harsh environmental conditions.4. Sensing and Perception4.1. The control center should be equipped with advanced sensing and perception technologies, including radar, lidar, and optical sensors.4.2. The system should be capable of detecting and tracking objects in real-time, including moving vehicles, humans, and natural obstacles.4.3. The sensing and perception capabilities should be able to operate in diverse weather and lighting conditions.5. Control and Decision-making5.1. The control center should have autonomous control and decision-making capabilities to ensure continuous and safe operation.5.2. The system should be able to dynamically adapt and respond to changing environments and situations.5.3. The control and decision-making processes should be transparent and auditable.6. Power and Energy6.1. The control center should have robust and reliable power and energy supply systems, including backup and emergency power sources.6.2. The system should be energy-efficient and capable of optimizing power usage for different operational scenarios.6.3. The power and energy systems should be resilient to potential disruptions and f本人lures.7. Cybersecurity7.1. The control center should implement state-of-the-art cybersecurity measures to protect ag本人nst unauthorized access, data breaches, and cyber-attacks.7.2. The system should have advanced encryption and authentication mechanisms to ensure the confidentiality and integrity of data.7.3. The cybersecurity measures shouldply with international standards and regulations.8. Human-Machine Interface8.1. The control center should provide an intuitive and user-friendly human-machine interface for operators and administrators.8.2. The interface should support multi-modal interaction, including touch screens, voicemands, and gesture recognition.8.3. The system should be designed to minimize cognitive load and enhance situational awareness for operators.9. M本人ntenance and Support9.1. The control center should have built-in diagnostic and monitoring capabilities for proactive m本人ntenance and support.9.2. The system should be easily upgradable and expandable to amodate future technological advancements.9.3. The m本人ntenance and support processes should be well-documented and standardized.10. ConclusionIn conclusion, the above technical requirements outline the fundamental capabilities and features that are essential for the successful operation of unmanned control centers in all-territory spaces. By adhering to these requirements, organizations and developers can ensure the reliability, efficiency, and safety ofunmanned control center systems, thereby contributing to the advancement of technology in the field of unmanned space control.。

关于定义自己的作文英文回答：I am a complex and multifaceted individual, a tapestry woven with threads of diverse experiences, beliefs, and aspirations. To define myself is to embark on an introspective journey, exploring the depths of my being and unraveling the intricate web of influences that shape my identity.At my core, I am an insatiable seeker of knowledge, an avid explorer of the vast realms of ideas and perspectives. My curiosity extends beyond the confines of any single discipline, leading me to embrace a multidisciplinary approach to learning. Whether delving into the intricacies of quantum physics, the nuances of ancient civilizations, or the complexities of human behavior, I find immense joy in expanding my understanding of the world around me.Inseparable from my intellectual pursuits is myunwavering commitment to empathy and compassion. I believe that true human connection transcends superficial differences and requires a deep appreciation for the unique experiences and perspectives of others. I strive to cultivate an open heart and a listening ear, seeking to understand the world from multiple vantage points and to lend a helping hand wherever I can.My identity is also deeply influenced by my cultural heritage and the values instilled in me from a young age. I am proud of my roots and the traditions that have shaped who I am today. While I am always open to new perspectives and experiences, I believe that it is important to honor and preserve the cultural legacy that I have inherited.Furthermore, I am a firm believer in the power of creativity and self-expression. I find solace and inspiration in artistic endeavors, whether it be writing, painting, or playing music. Through creative pursuits, I am able to explore my inner world, communicate my thoughts and emotions, and connect with others on a deeper level.In addition to my personal qualities and beliefs, my identity is also shaped by the relationships I have with others. My family, friends, and mentors have all played a significant role in molding my character and shaping my perspectives. I am deeply grateful for the love, support, and guidance that they have provided me throughout my life.As I continue to navigate the complexities of life, I am forever evolving and redefining my sense of self. I am open to new experiences, eager to learn and grow, and committed to living a life that is both fulfilling and meaningful. Ultimately, I aspire to be an individual who is compassionate, intellectually curious, culturally aware, creatively expressive, and deeply connected to both myself and others.中文回答：我是个复杂而多方面的人，就像一幅由各种经历、信仰和抱负交织而成的挂毯。

航天发射中心简介英语作文The Space Launch Center is a place where rockets are launched into space. It's a hub of activity with scientists, engineers, and astronauts working together to make sure everything goes smoothly.The center is equipped with state-of-the-art technology and facilities to support the launch process. From the control room, operators monitor the rocket's trajectory and make real-time adjustments to ensure a successful launch.Before a rocket is launched, it undergoes rigorous testing to ensure its safety and reliability. Engineers carefully inspect every component to make sure it meets the highest standards.Once the rocket is ready, astronauts prepare for their journey into space. They undergo extensive training to prepare for the challenges they will face in the harsh environment of outer space.When the countdown begins, there is an air of excitement and anticipation. Everyone is focused on the task at hand, knowing that the success of the mission depends on their collective efforts.As the rocket blasts off into the sky, it's a moment of triumph for everyone involved. The culmination of years of hard work and dedication has paid off, and the journey into space has begun.The Space Launch Center plays a crucial role in advancing our understanding of the universe and pushing the boundaries of human exploration. It's a place where dreams take flight and where the impossible becomes possible.。