a r X i v :q u a n t -p h /0504227v 2 7 M a y 2005,Quantum control of entanglement and information of two solid state qubits:remotecontrol of dephasingShang-Bin Li ∗and Jing-Bo XuChinese Center of Advanced Science and Technology (WorldLaboratory),P.O.Box 8730,Beijing,People’s Republic of China;andZhejiang Institute of Modern Physics and Department of Physics,Zhejiang University,Hangzhou 310027,People’s Republicof ChinaWe investigate the scheme for controlling information characterized by Von-Neumann entropy and the stationary state entanglement characterized by concurrence of two solid state qubits in the collective dephasing channel.It is shown that the local maximal value of the stationary state concurrence always corresponds to the local minimal value of information.We also propose a scheme for remotely controlling the entanglement of two solid state qubits against the collective dephasing.This idea may open a door to remotely suppress the detrimental effects of decoherence.PACS numbers:03.65.Ud,03.67.-a,05.40.CaI.INTRODUCTIONQuantum entanglement plays an important role in quantum information processes,which can exhibit the nature of a nonlocal correlation between quantum sys-tems that have no classical interpretation [1].Re-cently,it has been recognized that entanglement can be used as an important resource for quantum tele-portation or quantum computation.Ordinarily,entan-glement can be destroyed by the interaction between quantum systems of interest and its surrounding envi-ronments.Certain kind of the interaction between the physical system and environments or measuring appara-tus can lead to the collective dephasing,which occurs in the physical systems such as trapped ions,quantum dots.Collective dephasing allows the existence of the so-called decoherence-free subspace [2].Several strate-gies have been proposed to suppress the detrimental effects of decoherence,while at the same time allow-ing for robust manipulation of the quantum information [15,16,17,18,19,20,21,22,23,24,25],for example,the quantum error correction schemes [15,16,17,18,19,20],feedback implementations [21],quantum error avoiding approach [22,23],dynamical decoupling techniques [24],engineering of pointer state methods [25].Here,we pro-pose a scheme for remotely controlling the dephasing of two qubits.It is shown that,via a preexistent multi-partite entanglement and the quantum erasing process,we can remotely control the entanglement of two qubits in the collective dephasing channel.Recently,the quantum information processes in the presence of the collective dephasing have intrigued much attention [3,4,7,8].Khodjasteh and Lidar have investi-gated the universal fault-tolerant quantum computation in the presence of spontaneous emission and collective dephasing [3].Hill and Goan have studied the effect∂t=γ222 This paper is organized as follows:In section II,westudy the system in which one of two solid state qubits ina collective dephasing environment is driven by afinite-time externalfield.We compare the information char-acterized by Von-Neumann entropy and the entangle-ment characterized by concurrence of the stationary stateandfind that the local maximal value of the stationarystate concurrence always corresponds to the local mini-mal value of information.In section III,we investigatehow to remotely control the dephasing of two qubits bymaking use of a preexistent multi-partite entanglementand the quantum erasing process.In section IV,thereare some conclusions.RMATION AND ENTANGLEMENT INTHE STATIONARY STATE OF TWO SOLIDSTATE QUBITSHere,we investigate the model in which two solid statequbits are exposed in a collective dephasing channel andone of two qubits is simultaneously driven by afinite-time externalfield.The dynamics of two qubits can bedescribed by the following master equation∂ˆρ2[Ω1(t)ˆσ(1)x,ˆρ]+γγ,γT)|11 11|+b(Ω1γ,γT)|01 01|+d(Ω1γ,γT)|10 01|+f∗(Ω1γ=41.25.In this case,two qubitsare initially in the Bell state|Φ− .σy),where the asterisk indicates complex conjugation.The concurrence related to the density matrixρs can bewritten asC s=2max[0,|f(Ω1a(Ω1γ,γT)].(6)The information quantified by the Von-Neumann en-tropy of the stationary state of two qubits is defined byS=−Tr(ρs log2ρs).We can easily obtain the analyticalexpression of the information S as follows,S=−a log2a−d log2d−β+log2β+−β−log2β−,(7)whereβ±=b+c± 2.(8)Firstly,we consider the case in which two qubits are ini-tially in the Bell state|Φ− ,i.e.,the Bell singlet state.In Fig.1,the stationary state concurrence and the in-formation of the stationary state are plotted as the func-tion of the parameterγT.It is shown that the values ofthe scaled action timeγT which locally maximizes thestationary state entanglement always locally minimizesthe information.Both the information of the stationarystate and the stationary state concurrence oscillate withγT,which imply one can control both the entanglementand information of the stationary state of two qubits inthe collective dephasing environment by adjusting thescaled action timeγT of the locally drivingfield.Then,we consider the case in which two qubits are initiallyin the standard Werner state.The standard two-qubitWerner state was defined by[5]ρW=r|Φ− Φ−|+1−rΩ1state|Ψ .From Fig.3,we know that two qubits is sep-arable ifγT equals zero,which is different from the casewith the initial robust entangled state|Φ− .However, the correspondence between the local maximal value ofthe concurrence and the local minimal value of the in-can observeof twoand notthe entangle-state mayofestimations ofbeen proposed.suchstates withoutquantumTherefore,value ofen-us a morethe entan-controlmaking use ofand the quan-solid statequbit3,such polarized photon.initially in the √(where|H and3.If the qubitand one ofchannel isthe evolu-by Eq.(3),be obtained(Ω1|V 3 V|(Ω1|V 3 V|(Ω1|V 3 H|,(10)can be calcu-free qubit3 is simply traced out,the remaining two solid state qubits 1and2have not any entanglement in the stationary 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