量子退相干及其纠缠态的制备
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摘要
近些年来,以量子力学为基础的量子信息学以其独特的性质引起了人们广泛的关注,它显示了经典信息学所无法比拟的优越性,具有潜在的巨大应用价值,甚至会引起划时代的信息产业革命。量子信息科学中用量子态表示信息,由于量子态满足相干叠加原理,从而导致纠缠态的存在。为了利用纠缠,纠缠态的制备成为量子信息学中重要的研究内容,现今人们在实验上已经实现了一些重要的纠缠态,并取得了许多令人瞩目的成就,但是对多粒子纠缠的制备问题还处于不断的努力探索之中。
在实际的量子系统中,环境的影响是不可避免的。环境导致的量子退相干以及由此引发的退纠缠效应是实现通用量子计算机的绊脚石。因此,确切知道量子退相干是如何破坏物体的相干性,对量子信息科学发展至关重要。现今,量子退相干成为理论界和实验界的研究热点之一。
本文着重研究了量子退相干及多粒子纠缠态的制备问题,并进行了一些讨论,主要内容如下:
1、用短时近似方法研究了约瑟夫森电荷量子比特中的量子Hadamard门的退相干问题,我们发现最大偏离算子范数和先前文献有相同的表达式,并进一步说明了无论系统的初始态是什么,都能够在DiVincenzo低退相干的要求下,完成Hadamard门操作,从而证实了约瑟夫森装置是一个很好的量子计算装置。
2、在一般的自旋-玻色模型中,我们研究了混态纠缠的时间演化行为,并讨论了现今引起很大关注的纠缠猝死现象。结果表明,纠缠衰减不但依赖于温度而且依赖于环境和系统间的耦合强度,且混态纠缠衰减因子和纯态有相同的形式。
3、借助于主方程方法,我们讨论了EPR系统中与各自腔场相互作用的两粒子纠缠动力学问题,发现环境导致的纠缠猝死现象与系统的初始态以及平均光子数有关。通过对纠缠度量和系统能量转移的时间演化分析,我们得出最大纠缠度对应着EPR系统的最小能量,且它们之间的时间变化既不是一对一,也不是同步的关系,甚至在没有初始纠缠的情况下,仍有能量转移现象发生的结论。这从侧面反映出了,用能量变化来表征纠缠猝死现象至少在我们的模型中是行不通的。
4、通过分析腔场驱动下开放系统中的两能级双量子点的激子纠缠动力学,我们获得以激子-光子耦合g_(1,2)、声子布局数N_(1,2)、黄昆-里斯因子λ_(1,2)为变量的纠缠度量—concurrence的函数表达式,发现纠缠猝死现象可以通过这些相关的参数来调控,从中说明了抑制纠缠猝死的条件。
5、基于经典外场驱动的多原子微波腔量子电动力学系统,我们提出了一种产生多原子纠缠态的理论方案。该方案通过单步操作即可完成,由于采用了大失谐,所以被提议的量子操作对腔场衰减起到了免疫作用,因此可以赢得理想几率的cluster态。
The quantum information science basedon quantum theory has attracted a wide attention in recent years.It shows the superiorities that classical information is not to be compared with and has so many great potential applications that it may lead to a revolution in information domain.Quantum information is carried by quantum coherent superposition states,which induce the appearance of entangled states.In order to utilize the entanglement, the generation of entangled states lie at the heart of the quantum information. Now,various schemes of generating entangled states were proposed and some remarkable achievements were made.However,the preparation of multipartite entangled states are still under research.
It is well known,however,that the effect of environment on the quantum system,which may deteriorate the coherence and even leads to decoherence and disentanglement and becomes a major obstacle towards the realization of a universal quantum computer,must be taken into account in practical applications.So,it is important to understand the effect of decoherence on the development of the quantum information and much attention has been paid to the research about decoherence either in theories or in experiments, recently.
In our paper,we mainly investigate the decoherence,disentanglement and the generation schemes of multipartite entangled states in quantum computation.The results are following:
First,we investigate the short-time decoherence of a quantum Hadamard gate with the Josephson-junction device(JJD).It is shown that the maximum norm of the deviation operator has the same expression as in the previous literature.We demonstrate that the elementary gate operation can be completed under the low decoherence criterion no matter what the initial state is.Thus,the JJD can be a good candidate of quantum computating devices.
Second,we study the time-evolution of the mixed,state entanglement in a general spin-boson model including the entanglement sudden death.It is shown that the decay of entanglement depends on the temperature and coupling strength.Moreover the entanglement decay-factor of mixed states has the same form as that of the pure states.
Third,we study the entanglement dynamics of the Einstein,Podolsky and Rosen(EPR) system in which two spatially separated particles are coupled with their own cavity field.The environment-induced entanglement sudden death depends on the parameters of an initial entangled state and a mean photon number as well.We,moreover,investigate the time-evolution behaviour for both concurrence and energy transfer between the EPR particles and the environment,from which it is found that the maximal concurrence indeed corresponds to the minimal energy of the EPR system. However,their time variations are neither in one-to-one correspondence nor in step.Particularly when the state of two particles becomes disentangled,the time variation of energy transfer still exists.This observation suggests that the concurrence seems not directly related to the energy transfer at least for the model at hand.
Then,the entanglement dynamics of excitons in the two-level double-quantum-dot driven by cavity fields is investigated with the particular attention on the effect ofphonon bath which makes an open two-qubit system of the quantum-dot and cavity-field.The time-evolution of the concurrence, which is the entanglement measure of mixed states for the open system,is obtained explicitly as a parameter function of exciton-photon couplings g_(1,2), the phonon-populations N_(1,2) and the Huang-Rhys factorsλ_(1,2).The entanglement sudden death(ESD) is found and is seen to be manipulated by the parameters g_(1,2),N_(1,2) andλ_(1,2) as well.We moreover demonstrate the condition to suppress the ESD sufficiently.
Finally,we propose a potential scheme to generate cluster states with one-step operation based on cavity quantum electrodynamics in a multiatom and microwave cavity system with an additional driven classical field.The proposed quantum operation avoids cavity-field induced decay duo to large detuning and may achieve the cluster states with ideal success probability.
在实际的量子系统中,环境的影响是不可避免的。环境导致的量子退相干以及由此引发的退纠缠效应是实现通用量子计算机的绊脚石。因此,确切知道量子退相干是如何破坏物体的相干性,对量子信息科学发展至关重要。现今,量子退相干成为理论界和实验界的研究热点之一。
本文着重研究了量子退相干及多粒子纠缠态的制备问题,并进行了一些讨论,主要内容如下:
1、用短时近似方法研究了约瑟夫森电荷量子比特中的量子Hadamard门的退相干问题,我们发现最大偏离算子范数和先前文献有相同的表达式,并进一步说明了无论系统的初始态是什么,都能够在DiVincenzo低退相干的要求下,完成Hadamard门操作,从而证实了约瑟夫森装置是一个很好的量子计算装置。
2、在一般的自旋-玻色模型中,我们研究了混态纠缠的时间演化行为,并讨论了现今引起很大关注的纠缠猝死现象。结果表明,纠缠衰减不但依赖于温度而且依赖于环境和系统间的耦合强度,且混态纠缠衰减因子和纯态有相同的形式。
3、借助于主方程方法,我们讨论了EPR系统中与各自腔场相互作用的两粒子纠缠动力学问题,发现环境导致的纠缠猝死现象与系统的初始态以及平均光子数有关。通过对纠缠度量和系统能量转移的时间演化分析,我们得出最大纠缠度对应着EPR系统的最小能量,且它们之间的时间变化既不是一对一,也不是同步的关系,甚至在没有初始纠缠的情况下,仍有能量转移现象发生的结论。这从侧面反映出了,用能量变化来表征纠缠猝死现象至少在我们的模型中是行不通的。
4、通过分析腔场驱动下开放系统中的两能级双量子点的激子纠缠动力学,我们获得以激子-光子耦合g_(1,2)、声子布局数N_(1,2)、黄昆-里斯因子λ_(1,2)为变量的纠缠度量—concurrence的函数表达式,发现纠缠猝死现象可以通过这些相关的参数来调控,从中说明了抑制纠缠猝死的条件。
5、基于经典外场驱动的多原子微波腔量子电动力学系统,我们提出了一种产生多原子纠缠态的理论方案。该方案通过单步操作即可完成,由于采用了大失谐,所以被提议的量子操作对腔场衰减起到了免疫作用,因此可以赢得理想几率的cluster态。
The quantum information science basedon quantum theory has attracted a wide attention in recent years.It shows the superiorities that classical information is not to be compared with and has so many great potential applications that it may lead to a revolution in information domain.Quantum information is carried by quantum coherent superposition states,which induce the appearance of entangled states.In order to utilize the entanglement, the generation of entangled states lie at the heart of the quantum information. Now,various schemes of generating entangled states were proposed and some remarkable achievements were made.However,the preparation of multipartite entangled states are still under research.
It is well known,however,that the effect of environment on the quantum system,which may deteriorate the coherence and even leads to decoherence and disentanglement and becomes a major obstacle towards the realization of a universal quantum computer,must be taken into account in practical applications.So,it is important to understand the effect of decoherence on the development of the quantum information and much attention has been paid to the research about decoherence either in theories or in experiments, recently.
In our paper,we mainly investigate the decoherence,disentanglement and the generation schemes of multipartite entangled states in quantum computation.The results are following:
First,we investigate the short-time decoherence of a quantum Hadamard gate with the Josephson-junction device(JJD).It is shown that the maximum norm of the deviation operator has the same expression as in the previous literature.We demonstrate that the elementary gate operation can be completed under the low decoherence criterion no matter what the initial state is.Thus,the JJD can be a good candidate of quantum computating devices.
Second,we study the time-evolution of the mixed,state entanglement in a general spin-boson model including the entanglement sudden death.It is shown that the decay of entanglement depends on the temperature and coupling strength.Moreover the entanglement decay-factor of mixed states has the same form as that of the pure states.
Third,we study the entanglement dynamics of the Einstein,Podolsky and Rosen(EPR) system in which two spatially separated particles are coupled with their own cavity field.The environment-induced entanglement sudden death depends on the parameters of an initial entangled state and a mean photon number as well.We,moreover,investigate the time-evolution behaviour for both concurrence and energy transfer between the EPR particles and the environment,from which it is found that the maximal concurrence indeed corresponds to the minimal energy of the EPR system. However,their time variations are neither in one-to-one correspondence nor in step.Particularly when the state of two particles becomes disentangled,the time variation of energy transfer still exists.This observation suggests that the concurrence seems not directly related to the energy transfer at least for the model at hand.
Then,the entanglement dynamics of excitons in the two-level double-quantum-dot driven by cavity fields is investigated with the particular attention on the effect ofphonon bath which makes an open two-qubit system of the quantum-dot and cavity-field.The time-evolution of the concurrence, which is the entanglement measure of mixed states for the open system,is obtained explicitly as a parameter function of exciton-photon couplings g_(1,2), the phonon-populations N_(1,2) and the Huang-Rhys factorsλ_(1,2).The entanglement sudden death(ESD) is found and is seen to be manipulated by the parameters g_(1,2),N_(1,2) andλ_(1,2) as well.We moreover demonstrate the condition to suppress the ESD sufficiently.
Finally,we propose a potential scheme to generate cluster states with one-step operation based on cavity quantum electrodynamics in a multiatom and microwave cavity system with an additional driven classical field.The proposed quantum operation avoids cavity-field induced decay duo to large detuning and may achieve the cluster states with ideal success probability.
引文
[1]苏晓琴,郭光灿,量子通信与量子计算团,量子电子学报,21(2004)706.
[2]A.Yao,In Procedings of the 34th Annual Symposium of Foundation of Computer Science(1993) 352.
[3]A.Barenco,C.H.Bennett,R.Cleve,D.P.DiVincenzo,N.Margolus,P.Shor,et al.,Elementary gates for quantum computation,Phys.Rev.A 52(1995) 3457.
[4]C.Monroe,D.M.Meekhof,B.E.King,et al.,Demonstration of a Fundamental Quantum Logic Gate,Phys.Rev.Lett.75(1995) 4714.
[5]A.Rauschenbeutel,G.Nogues,S.Osnaghi,P.Bertet,M.Brune,J.M.Raimond,and S.Haroche,Coherent Operation of a Tunable Quantum Phase Gate in Cavity QED,Phys.Rev.Lett.83(1999) 5166.
[6]J.K.Pathos and P.L.Knight,Quantum Computation with a One-Dimensional Optical Lattice,Phys.Rev.Lett.91(2003) 107902.
[7]H.Ollivier and P.Milman,Proposal for realization ofa Toffoli gate via cavity-assisted collision,e-print quant-ph/0306064.
[8]J.Zhang,W.Liu,Z.Deng,Z.Lu,and G.L.Long,Modularization of a multi-qubit controlled phase gate and its nuclear magnetic resonance implementation,J.Opt.B 7(2005) 22.
[9]C.P.Yang and S.Han,n-qubit-controlled phase gate with superconducting quantum-interference devices coupled to a resonator,Phys.Rev.A 72(2005) 032311.
[10]X.B.Zou,K.Li,and G.C.Guo,Linear optical scheme for direct implementation of a nondestructive N-qubit controlled phase gate,Phys.Rev.A 74(2006) 044305.
[11]C.H.Bennett,G.Brassard,C.Crepeau,R.Jozsa,A.Peres,and W.K.Wootters,Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,Phys.Rev.Lett.70(1993)1895.
[12]D.Bouwmeester,J.W.Pan,K.Mattle,M.Eibl,H.Weinfurter,A.Zeilinger,Experimental quantum teleportation,Nature 390(1998) 575.
[13]D.Boschi,S.Branca,F.De Martini,L.Hardy,and S.Popescu,Experimental Realization of Teleporting an Unknown Pure Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels,Phys.Rev.Lett.80(1998) 1121.
[14]A.Furusawa,J.L.Sorensen,S.L.Braunstein,C.A.Fuchs,H.J.Kimble,E.S.Polzik,Unconditional quantum teleportation,Science 282(1998) 706.
[15]Yu.A.Chen,S.Chen,Z.S.Yuan,B.Zhao,C.S.Chuu,J.Schmiedmayer,J.W.Pan,Memory-built-in quantum teleportation with photonic and atomic qubits,Nature Physics 4(2008)103.
[16]W.H.Zurek,Pointer basis of quantum apparatus:Into what mixture dose the wave packet collapse,Phys.Rev.D,24(1981) 1516.
[17]W.H.Zurek,Envionment-induced superselection rules,Phys.Rev.D,26(1982)1862.
[18]R.Kubo,Note on the stochastic theory of resonance absorption,J.Phys.Soc.Jap.9,(1954) 935.
[19]G.J.Milburn,Intrinsic decoherence in quantum mechanics,Phys.Rev.A 44(1991)5401.
[20]H.D.Zeh,Found Phys,1(1970) 69.
[21]曾谨言,裴寿镛主编.量子力学新进展[M]:第一辑.北京:北京大学出版社,2000,59-127.
[22]P.Zhang,X.F.Liu,C.P.Sun Consisitent approach for quantum measurement,Phys.Rev.A 66(2002) 042104.
[23]C.J.Myatt,B.Q.King,A.Turchette et al.,Nature,403(2000) 269.
[24]P.W.Anderson,A Mathematical Model for the Narrowing of Spectral Lines by Exchange or Motion,J.Phys.Soc.Jap 9(1954) 316.
[25]V.Buzek and M.Konopka,Dynamics of open systems governed by the Milburn equation,Phys.Rev.A 58(1998) 1735.
[26] M. Schlosshauer, Self-induced decoherence approach: Strong limitations on its validity in a simple spin bath model and on its general physical relevance, Phys. Rev. A 72 (2005)012109.
[27] Renato M. Angelo, E. S. Cardoso and K. Furuya, Decoherence induced by a phase-damping reservoir, Phys. Rev. A 73 (2006) 062107.
[28] Xian-Ting Liang, Non-Markovian dynamics and phonon decoherence of a double quantum dot charge qubit, Phys. Rev. B 72 (2005) 245328.
[29] Michael Thorwart and Peter Hanggi, Decoherence and dissipation during a quantum XOR gate operation, Phys. Rev. A 65 (2002) 012309.
[30] Pochung Chen, Dynamical decoupling-induced renormalization of non-Markovian dynamics, Phys. Rev. A 75 (2007) 062301.
[31] Adrian A. Budini, Random Lindblad equations from complex environments, Phys. Rev. E 72 (2007) 056106.
[32] S. Maniscalco, Complete positivity of a spin-112 master equation with memory, Phys. Rev. A 75 (2007) 062103.
[33] D. F. Walls and G J. Milburn, Effect of dissipation on quantum coherence, Phys. Rev. A 31 (1985)2403.
[34] D. N(?)ller, L. B. Madsen, and K. Malmer, Geometric phases in open tripod systems, Phys. Rev. A 77 (2008) 022306.
[35] Gregory A. Fiete and Eric J. Heller, Semiclassical theory of coherence and decoherence, Phys. Rev. A 68 (2003) 022112.
[36] J. I. Kim, M. C. Nemes, A. F. de Toledo Piza, and H. E. Borges, Perturbative Expansion for Coherence Loss, Phys. Rev. Lett. 77 (1996) 207.
[37] C. W. Gardiner, P. Zoller, Quantum Noise, 2000, Springer-Verlag, Berlin.
[38] W.G Unruh, Experimental Study of High-Beta Tokamak Stability, Phys. Rev. A 51, (1995)992.
[39] O. Astafiev, Yu. A. Pashkin, Y. Nakamura, T. Yamamoto, and J. S. Tsai, Quantum Noise in the Josephson Charge Qubit, Phys. Rev. Lett. 93 (2004) 267007.
[40] S. Vorojtsov, E. R. Mucciolo, and Harold U. Baranger, Phonon decoherence of a double quantum dot charge qubit, Phys. Rev. B 71 (2005) 205322.
[41] T. Hayashi, T. Fujisawa, H. D. Cheong, Y. H. Jeong, and Y. Hirayama, Coherent Manipulation of Electronic States in a Double Quantum Dot, Phys. Rev. Lett. 91 (2003)226804; J. R. Petta, A. C. Johnson, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Manipulation of a Single Charge in a Double Quantum Dot, Phys. Rev. Lett. 93 (2004) 186802.
[42] M. Thorwart, J. Eckel, and E. R. Mucciolo. Non-Markovian dynamics of double quantum dot charge qubits due to acoustic phonons, Phys. Rev. B 72 (2005) 235320.
[43] D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, et al., Experimental issues in coherent quantum-state manipulation of trapped atomic ions, J. Res. Natl Inst. Stand. Tech. 103 (1998) 259.
[44] A. M. Steane, Error Correcting Codes in Quantum Theory, Phys. Rev. Lett. 77(1996) 793.
[45] A. R. Calderbank and Peter W. Shor, Good quantum error-correcting codes exist, Phys. Rev. A 54 (1996) 1098.
[46] Lev Ioffe and Marc Mezard, Asymmetric quantum error-correcting codes, Phys. Rev. A 75 (2007)032345.
[47] Lu-Ming Duan and Guang-Can Guo, Preserving Coherence in Quantum Computation by Pairing Quantum Bits, Phys. Rev. Lett. 79 (1997) 1953.
[48] H. Wei, Z. J. Deng,. X. L. Zhang, and M. Feng, Transfer and teleportation of quantum states encoded in decoherence-free subspace, Phys. Rev. A 76 (2007) 054304.
[49] L. Viola and S. Lloyd, Dynamical suppression of decoherence in two-state quantum systems, Phys. Rev. A 58 (1998) 2733.
[50] J. Bergli and L. Faoro, Exact solution for the dynamical decoupling of a qubit with telegraph noise, Phys. Rev. B 75 (2007) 054515.
[51] K. Shiokawa and D. A. Lidar, Dynamical decoupling using slow pulses: Efficient suppression of 1/f noise, Phys. Rev. A 69 (2004) 030302.
[52] D. A. Lidar, D. Bacon, and K. B. Whaley, Concatenating Decoherence-Free Subspaces with Quantum Error Correcting Codes, Phys. Rev. Lett. 82 (1999) 4556.
[53]M.S.Byrd,D.A.Lidar,L.A.Wu,and P.Zanardi,Universal leakage elimination,Phys.Rev.A 71(2005) 052301.
[54]Y.Zhang,Z.W.Zhou,B.Yu,and G.C.Guo,Concatenating dynamical decoupling with decoherence-free subspaces for quantum computation,Phys.Rev.A 69(2004)042315.
[55]A.Einstein,B.Podolsky,N.Rosen,Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Phys.Rev.47(1935) 777.
[56]Schr(o|¨)dinger,Naturwissenschaften,23(1935) 807.
[57]D.Bohm,量子理论,侯得彭译,北京,商务印书馆,1982.
[58]J.S.Bell,Physics 1(1964)195.
[59]A.Aspect,P.Grangier,and G.Roger,Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment:A New Violation of Bell's Inequalities,Phys.Rev.Lett.49(1982) 91.
[60]A.Aspect,J.Dalibard,and G.Roger,Experimental Test of Bell's Inequalities Using Time- Varying Analyzers,Phys.Rev.Lett.49(1982) 1804.
[61]M.A.Nielsen,I.L.Chuang,Quantum Computation and Quantum InformationCambridge University Press,Cambridge,(2000).
[62]李承祖等,量子通信与量子计算,长沙:国防科技大学出版社,2000:8.
[63]V.Vedarl,et al.,Quantifying Entanglement,Phys.Rev.Lett.78(1997) 2275.
[64]M.Horodecki,P.Horodecki,R.Horodecki,Separability of mixed quantum states:linear contractions approach,Open Syst.Inf.Dyn.13(2006) 103.
[65]W.K.Wootters,Entanglement of Formation of an Arbitrary State of Two Qubits,Phys.Rev.Lett.80(1998) 2245.
[66]P.Rungtal,V.Buzek,C.M.Caves,M.Hiilery,and G.J.Milbum,Universal state inversion and concurrence in arbitrary dimensions,Phys.Rev.A 64(2001) 042315.
[67]S.Albeverio,and S.M.Fei,A note on invariants and entanglements,J.Opt.B 3(2001) 223.
[68]A.Peres,Separability Criterion for Density Matrices,Phys.Rev.Lett.77(1996) 1413.
[69]G.Vidal and R.F.Werner,Computable measure of entanglement,Phys.Rev.A 65 (2002)032314.
[70] T. Wei and P. Goldbart, Geometric measure of entanglement and applications to bipartite and multipartite quantum states, Phys. Rev. A 68 (2003) 042307.
[71] T. Wei, M. Ericsson, P. Goldbart and W. Munro, Quant. Inf. Comput. 4 (2004) 252.
[72] D. A. Meyer, and N. R. Wallach, J. Math. Phys, 43 (2002) 4273.
[73] F. Verstraete, M. Popp, and J. I. Cirac, Entanglement versus Correlations in Spin Systems, Phys. Rev. Lett. 92 (2004) 027901.
[74] D. M. Greenberger, M. A. Home, A. Shimony, and A. Zeilinger, Bell theorem without inequalities, Am. J. Phys. 58 (1990) 1131.
[75] W. Dur, G. Vidal, and J. 1. Cirac, Three qubits can be entangled in two inequivalent ways, Phys. Rev. A 62 (2000) 062314.
[76] R. F. Werner, Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model, Phys. Rev. A 40 (1989) 4277.
[77] C. H. Bennett, G. Brassard, S. Popescu, et al., Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels, Phys. Rev. Lett. 76 (1996) 722.
[78] H. J. Briegel and R. Raussendorf, Persistent Entanglement in Arrays of Interacting Particles, Phys. Rev. Lett. 86 (2001) 910.
[79] C. Sackett, D. Kielpinski, B. King, et al., Experimental entanglement of four particles, Nature (London) 404 (2000) 256.
[80] A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J. Raimond, and S. Haroche, Step-by-Step Engineered Multiparticle Entanglement, Science, 288 (2000) 2024.
[81] I. L. Chuang, N. Gershenfeld, and M. Kubinec, Experimental Implementation of Fast Quantum Searching, Phys. Rev. Lett. 80 (1998) 3408.
[82] E. Knill, R. Laflamme, R. Martinez, C.-H. Tseng, An algorithmic benchmark for quantum information processing, Nature (London) 404 (2000) 368.
[83] D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, Observation of Three-Photon Greenberger-Horne-Zeilinger Entanglement, Phys. Rev. Lett. 82 (1999) 1345.
[84] M. G. Moore and P. Meystre, Generating Entangled Atom-Photon Pairs from Bose-Einstein Condensates, Phys. Rev. Lett. 85 (2000) 5026.
[85] A. S0rensen, L.-M. Duan, J. I. Cirac, P. Zoller, Many-particle entanglement with Bose-Einstein condensates, Nature (London) 409 (2001) 63.
[86] P. K. Day, H. G. LeDuc, B. A. Mazin, A. Vayonakis and J. Zmuidzinas, A broadband superconducting detector suitable for use in large arrays, Nature (London) 425 (2003) 817.
[1]M.A.Nielsen,I.L.Chuang,Quantum Computation and Quantum Information,Cambridge University Press,Cambridge,2000.
[2]R.Raussendorfand Hans J.Briegel,A One-Way Quantum Computer,Phys.Rev.Lett.86(2001) 5188.
[3]P.Walther,K.J.Resch,T.Rudolph,E.Schenk,H.Weinfurter,V.Vedral,M.Aspelmeyer,and A.Zeilinger,Experimental one-way quantum computing,Nature (London) 434 (2005)169.
[4] N. Kiesel, C. Schmid, U. Weber, G. Toth, O. Guhne, R. Ursin, and H. Weinfurter, Experimental Analysis of a Four-Qubit Photon Cluster State, Phys. Rev. Lett. 95 (2005)210502.
[5] G. Vallone, E. Pomarico, P. Mataloni, F. De Martini, and V. Berardi, Realization and Characterization of a Two-Photon Four-Qubit Linear Cluster State, Phys. Rev. Lett. 98(2007)180502.
[6] M. S. Tame, R. Prevede, M. Paternostro, P. Bohi, M. S. Kim, and A. Zeilinger, Experimental Realization of Deutsch's Algorithm in a One-Way Quantum Computer, Phys. Rev. Lett. 98 (2007) 140501.
[7] S. Das, R. Kobes, and G. Kunstatter, Adiabatic quantum computation and Deutsch's algorithm, Phys. Rev. A 65 (2002) 062310.
[8] A. M. Childs, E. Farhi, and J. Preskill, Robustness of adiabatic quantum computation, Phys. Rev. A 65 (2002) 012322.
[9] D. P. Divincenzo, Quantum Computation, Science 270 (1995) 255; Two-bit gates are universal for quantum computation, Phys. Rev. A 51 (1995) 1015.
[10] A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, Elementary gates for quantum computation, Phys. Rev. A 52 (1995) 3457.
[11] D. DiVincenzo, "The physical implementation of quantum computation," Fortschr. Phys. 48 (2000) 771.
[12] DiVincenzo, D., 1997, in Mesoscopic Electron Transport, edited by L. Kouwenhoven, G. Schon, and L. Sohn, NATO AST Series E: Applied Sciences No. 345 (Kluwer Academic, Dordrecht), p. 657.
[13] T. P. Orlando, J. E. Mooij, Lin Tian, Caspar H. van der Wal, L. S. Levitov, Seth Lloyd, and J. J. Mazo, Superconducting persistent-current qubit, Phys. Rev. B 60, (1999) 15398.
[14] M. Grajcar, A. Izmalkov, S. H. van der Ploeg, S. Linzen, T. Plecenik, Th. Wagner, et al, Four-Qubit Device with Mixed Couplings, Phys. Rev. Lett. 96 (2006) 047006.
[15] L. F. Wei, J. R. Johansson, L. X. Cen, S. Ashhab, and Franco Nori, Controllable Coherent Population Transfers in Superconducting Qubits for Quantum Computing, Phys. Rev. Lett. 100 (2008) 113601.
[16] Y. Nakamura, Yu. A. Pashkin, and J. S. Tsai, Coherent control of macroscopic quantum states in a singleCooper-pair box, Nature (London), 398 (1999) 786.
[17] T. Yamamoto, Yu.A. Pashkin, O. Astafiev, Y. Nakamura and J.S. Tsai, Demonstration of conditional gate operation using superconducting charge qubits, Nature 425 (2003) 941.
[18] G. Burkard, D. Loss, and D. P. DiVincenzo, Coupled quantum dots as quantum gates, Phys. Rev. B 59 (1999) 2070.
[19] T. Tanamoto, Quantum gates by coupled asymmetric quantum dots and controlled-NOT-gate operation, Phys. Rev. A 61 (2000) 022305.
[20] T. Sleator and H. Weinfurter, Realizable Universal Quantum Logic Gates, Phys. Rev. Lett. 74 (1995) 4087.
[21] Y. F. Xiao, X. M. Lin, J. Gao, Y. Yang, Z. F. Han, and G.-C. Guo, Realizing quantum controlled phase flip through cavity QED, Phys. Rev. A 70 (2004) 042314.
[22] V. Giovannetti, D. Vitali, P. Tombesi, and A. Ekert, Scalable quantum computation with cavity QED systems, Phys. Rev. A 62 (2000) 032306.
[23] M. C. de Oliveira and W. J. Munro, Quantum computation with mesoscopic superposition states, Phys. Rev. A 61 (2000) 042309.
[24] L. M. K. Vandersypen and I. L. Chuang, NMR techniques for quantum control and computation, Rev. Mod. Phys. 76 (2004)1037.
[25] L. M. Vandersypen, M. Steffen, G. Breyta, C. S. Yannoni, R. Cleve, and I. L. Chuang, Experimental Realization of an Order-Finding Algorithm with an NMR Quantum Computer, Phys. Rev. Lett. 85 (2000) 5452.
[26] A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J. M. Raimond, and S. Haroche, Coherent Operation of a Tunable Quantum Phase Gate in Cavity QED, Phys. Rev. Lett. 83 (1999) 5166.
[27] G. W. Lin, X. B. Zou, M.-Y. Ye, X.-M. Lin, and G.-C. Guo, Scheme for tunable quantum phase gate and effective preparation of graph-state entanglement, Phys. Rev. A 77 (2008)032308.
[28] Z. J. Deng, X. L. Zhang, H. Wei, K. L. Gao, and M. Feng, Implementation of a nonlocal N -qubit conditional phase gate by single-photon interference, Phys. Rev. A 76 (2007) 044305.
[29] S. B. Zheng and G.-C. Guo, Efficient Scheme for Two-Atom Entanglement and Quantum Information Processing in Cavity QED, Phys. Rev. Lett. 85 (2000) 2392.
[30] O. Zilberberg, B. Braunecker, and D. Loss, Controlled-NOT gate for multiparticle qubits and topological quantum computation based on parity measurements, Phys.Rev.A 77 (2008) 012327.
[31] N. Sangouard, X. Lacour, S. Guerin, and H. R. Jauslin, Fast SWAP gate by adiabatic passage, Phys. Rev. A 72 (2005) 062309.
[32] B. Wang and L.-M. Duan, Implementation scheme of controlled SWAP gates for quantum fingerprinting and photonic quantum computation, Phys. Rev. A 75 (2007) 050304.
[33] M. Thorwart and P. Hanggi, Decoherence and dissipation during a quantum XOR gate operation, Phys. Rev. A 65 (2002) 012309.
[34] Markus J. Storcz and Frank K. Wilhelm, Decoherence and gate performance of coupled solid-state qubits, Phys. Rev. A 67 (2003) 042319.
[35] C. D. Hilll, and H. S.Goan, Gates for the Kane quantum computer in the presence of dephasing, Phys. Rev. A 70 (2003) 022310.
[36] E. Charron, E. Tiesinga, F. Mies, and C. Williams, Optimizing a Phase Gate Using Quantum Interference, Phys.Rev.Lett. 88 (2002) 077901.
[37] H. Wei, Z. J. Deng, X. L. Zhang, and M. Feng, Transfer and teleportation of quantum states encoded in decoherence-free subspace, Phys. Rev. A 76 (2007) 054304.
[38] Shi-Biao Zheng, Quantum-information processing and multiatom-entanglement engineering with a thermal cavity, Phys. Rev. A 66, 060303 (2002).
[39] Y. Makhlin, G. Schon, A. Shnirman, Quantum-state engineering with Josephson-junction devices, Rev. Mod. Phys. 73 (2001) 357.
[40] J. I. Cirac, P. Zoller, Quantum Computations with Cold Trapped Ions, Phys. Rev. Lett. 74(1995)4091.
[41] Y. C. Cheng, R. Silbey, Stochastic Liouville equation approach for the effect of noise in quantum computations, Phys. Rev. A 69 (2004) 052325.
[42] C. P. Sun, H. Zhan, and X. F. Liu, Decoherence and relevant universality in quantum algorithms via a dynamic theory for quantum measurement, Phys. Rev. A 58 (1998) 1810.
[43] A. Fedorov, L. Fedichkin, V. Privman, Evaluation of Decoherence for Quantum Control and Computing, J. Comp. Theor. Nanosci. 1, 132 (2004); L. Fedichkin, A. Fedorov, V. Privman, Measures of Decoherence, Proc. SP1E 5105 (2003) 243.
[44] I. L. Chuang, N.A. Gershenfeld, M. Kubinec, Experimental Implementation of Fast Quantum Searching, Phys. Rev. Lett. 80 (1998) 3408.
[45] E. Knill, R. Laflamme, R. Martinez, C.-H. Tseng, An algorithmic benchmark for quantum information processing, Nature 404 (2000) 368.
[46] T. Pellizzari, S.A. Gardiner, J.I. Cirac, P. Zoller, Decoherence, Continuous Observation, and Quantum Computing: A Cavity QED Model, Phys. Rev. Lett. 75 (1995)3788.
[47] D. Loss, D.P. Divincenzo, Quantum computation with quantum dots, Phys. Rev. A 57 (1998)120.
[48] K. Kimm, H. wang-h. Kwon, Decoherence of the quantum gate in Milburn's model of decoherence, Phys. Rev. A 65 (2002) 022311.
[49] D. Ahn, J.H. Oh, K. Kimm, S.W. Hwang, Time-convolutionless reduced-density-operator theory of a noisy quantum channel: Two-bit quantum gate for quantum-information processing, Phys. Rev. A 61 (2000) 052310.
[50] J. F. Poyatos, J. I. Cirac, P. Zoller, Complete Characterization of a Quantum Process: The Two-Bit Quantum Gate, Phys. Rev. Lett. 78 (1997) 390.
[51] X. T. Liang, Short-time decoherence of Josephson charge qubits, Phys. B 362 (2005) 243.
[52] D.Tolkunov, V.Privman, Short-time decoherence for general system-environment interactions, Phys. Rev. A 69 (2004) 062309.
[53] L. Viola, S. Lloyd, Dynamical suppression of decoherence in two-state quantum systems, Phys. Rev. A 58 (1998) 2733.
[54] G. Massimo Palma, K.-A. Suominen, A.K. Ekert, Quantum computation and dissipation, Proc. R. Soc. Lond. A 452 (1996) 567.
[55] L. Fedichkin, A. Fedorov, Error rate of a charge qubit coupled to an acoustic phonon reservoir, Phys. Rev. A 69 (2004) 032311.
[1]M.Schlosshauer,Decoherence,the measurement problem,and interpretations of quantum mechanics,Rev.Mod.Phys.76(2005)1267.
[2]张永德,量子信息物理原理,科学出版社,2006.
[3]D.Braun,Creation of Entanglement by Interaction with a Common Heat Bath,Phys.Rev.Lett.89(2002) 277901.
[4]F.Benatti,R.Floreanini and M.Piani,Environment Induced Entanglement in Markovian Dissipative Dynamics,Phys.Rev.Lett.91(2003) 070402.
[5]A.Hutton and S.Bose,Mediated entanglement and correlations in a star network of interacting spins,Phys.Rev.A 69(2004) 042312.
[6]Y.Hamdouni,M.Fannes,and F.Petruccione,Exact dynamics of a two-qubit system in a spin star environment,Phys.Rev.B 73(2006) 245323.
[7]Xiao-Zhong Yuan,Hsi-Sheng Goan,and Ka-Di Zhu,Non-Markovian reduced dynamics and entanglement evolution of two coupled spins in a quantum spin environment, Phys. Rev. B 75 (2007) 045331.
[8] M. A. Nielsen, I. L. Chuang, Quantum Computation and Quantum Information, Cambridge Univ. Press, 2000.
[9] C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels, Phys. Rev. Lett. 70 (1993) 1895; G. Rigolin, Quantum teleportation of an arbitrary two-qubit state and its relation to multipartite entanglement, Phys. Rev. A 71 (2005) 032303.
[10] C. H. Bennett, S. J. Wiesner, Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states, Phys. Rev. Lett. 69 (1992) 2881.
[11] A. K. Ekert, Quantum cryptography based on Bell's theorem, Phys. Rev. Lett. 67 (1991)661; M. Curty, M. Lewenstein, N. Lukenhaus, Entanglement as a Precondition for Secure Quantum Key Distribution, Phys. Rev. Lett. 92 (2004) 217903; K. Inoue, C. Santori, E. Waks, Y. Yamamoto, Entanglement-based quantum key distribution without an entangled-photon source, Phys. Rev. A 67 (2003) 062319.
[12] C. H. Bennett, H. J. Bernstein, S. Popescu, B. Schumacher, Concentrating partial entanglement by local operations, Phys. Rev. A 53 (1996) 2046.
[13] A. Peres, Quantum Theory: Concepts and Methods, Kluwer Academic, Boston, 1995.
[14] T. Yu, J. H. Eberly, Phonon decoherence of quantum entanglement: Robust and fragile states, Phys. Rev. B 66 (2002) 193306;
[15] T. Yu, J. H. Eberly, Qubit disentanglement and decoherence via dephasing, Phys. Rev. B 68 (2003)165322;
[16] T. Yu, J. H. Eberly, Finite-Time Disentanglement Via Spontaneous Emission, Phys. Rev. Lett. 93 (2004) 140404.
[17] V. Privman, D. Tolkunov, Decoherence and loss of entanglement, Proceeding of SPIE 5815 (2005)187; D. Tolkunov, V. Privman, P. K. Aravind, Decoherence of a measure of entanglement, Phys. Rev. A 71 (2005) 060308.
[18] K. Roszak, P. Machnikowski, Complete disentanglement by partial pure dephasing,Phys. Rev. A 73 (2006) 022313; A. Jamroz, Local aspects of disentanglement induced by spontaneous emission, quant-ph/0602128.
[19] R. Andre, R. Carvalho, F. Mintert, S. Palzer, A. Buchleitner, Entanglement dynamics under decoherence: from qubits to qudits, quant-ph/0508114.
[20] T. Yu, J. H. Eberly, Sudden Death of Entanglement: Classical Noise Effects, Opt. Commun. 264 (2006) 393.
[21] M. Yonac, T. Yu, J. H. Eberly, Sudden Death of Entanglement of Two Jaynes-Cummings Atoms, J. Phys. B 39 (2006) 621
[22] C. Pineda, T. H. Seligman, Evolution of pairwise entanglement in a coupled n-body system,Phys. Rev. A 73 (2006) 012305.
[23] X.-T. Liang, Initial decoherence and disentanglement of open two-qubit systems,Phys. Lett. A 349 (2006) 98.
[24] Asma Al-Qasimi and Daniel F. V. James, Sudden death of entanglement at finite temperature, Phys. Rev. A 77 (2008) 012117.
[25] Manzoor Ikram, Fu-li Li, and M. Suhail Zubairy, Disentanglement in a two-qubit system subjected to dissipation environments, Phys. Rev. A 75 (2007) 062336.
[26] Xiufeng Cao and Hang Zheng, Non-Markovian disentanglement dynamics of a two-qubit system, Phys. Rev. A 77 (2008) 022320.
[27] B. Bellomo, R. Lo Franco, and G. Compagno, Non-Markovian Effects on the Dynamics of Entanglement, Phys. Rev. Lett, 99 (2007) 160502.
[28] M. Yonac, T. Yu, J. H. Eberly, Sudden Death of Entanglement of Two Jaynes-Cummings Atoms, J. Phys. B 39 (2006) 621
[29] Zhi-Jian Li, Jun-Qi Li, Yan-Hong Jin and Yi-Hang Nie, Time evolution and transfer of entanglement between an isolated atom and a Jaynes-Cummings atom, J. Phys. B, 40 (2007) 3401.
[30] Ru-Fen Liu and Chia-Chu Chen, Role of the Bell singlet state in the suppression of disentanglement, Phys. Rev. A 74 (2006) 024102.
[31] T. Yu and J. H. Eberly, Quantum Open System Theory: Bipartite Aspects, Phys.Rev. Lett 97 (2006) 140403.
[32] M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, L. Davidovich, Environment-Induced Sudden Death of Entanglement, Science, 316(2007)579.
[33] A. R. P. Rau, Mazhar Ali, G. Alber, Hastening, delaying, or averting sudden death of quantum entanglement, EPL, 82 (2008) 40002.
[34] Marcelo O Terra Cunha, The geometry of entanglement sudden death, New Journal of Physics 9 (2007) 237.
[35] Ting Yu, Entanglement decay versus energy change: A model, Physics Letters A 361 (2007) 287.
[36] H. T. Cui , K. Li, X.X. Yi, A study on the sudden death of entanglement, Physics Letters A 365 (2007) 44.
[37] L. Aolita, R. Chaves, D. Cavalcanti, A. Aci n, and L. Davidovich, Scaling Laws for the Decay of Multiqubit Entanglement, Phys. Rev. Lett. 100 (2008) 080501.
[38] X. Q. Su, A. M. Wang, X. S. Ma and L. Qiu, Entanglement sudden death in a spinchannel, J. Phys. A 40 (2007) 11385.
[39] Z. Sun and X. G. Wang, Disentanglement in a quantum-critical environment, Phys. Rev. A 75 (2007) 062312.
[40] X. S. Ma, An M. Wang, and Y. Cao, Entanglement evolution of three-qubit states in a quantum-critical environment, Phys. Rev. B 76 (2007) 155327.
[41] Jun-Qi Li, Zhi-Jian Li, C. Gang, J.-Q. Liang, Time-evolving disentanglement in a spin-boson model, Physics Letters A 359 (2006) 275.
[42] W. K. Wootters, Entanglement of Formation of an Arbitrary State of Two Qubits, Phys. Rev. Lett. 80 (1998) 2245.
[43] C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, W. K. Wootters, Mixed-state entanglement and quantum error correction, Phys. Rev. A 54 (1996) 3824.
[44] V. Vedral, M. B. Plenio, M. A. Rippin, P.L. Knight, Quantifying Entanglement, Phys. Rev. Lett. 78 (1997) 2275.
[45] A. Peres, parability Criterion for Density Matrices, Phys. Rev. Lett. 77 (1996) 1413; K. Zyczkowski, P. Horodecki, A. Sanpera, M. Lewenstein, Volume of the set of separable states, Phys. Rev. A 58 (1998) 883.
[46] G. Lagmago Kamta, A.F. Starace, Anisotropy and Magnetic Field Effects on the Entanglement of a Two Qubit Heisenberg XY Chain, Phys. Rev. Lett. 88 (2002) 107901.
[47] R. Werner, Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model, Phys. Rev. A 40 (1989) 4277.
[48] R. Horodecki, M. Horodecki, Information-theoretic aspects of inseparability of mixed states, Phys. Rev. A 54 (1996) 1838.
[49] H. J. Carmichael, Statistical methods in quantum optics Master Equations and Fokker-Planck Equations (Berlin: Springer) (1999) pp 232-3.
[50] J. S. Pratt, Universality in the Entanglement Structure of Ferromagnets, Phys. Rev. Lett. 93 (2004) 237205.
[51] R. H. Dicke, Coherence in Spontaneous Radiation Processes, Phys. Rev. 93 (1954) 99; F. Haake and R. J. Glauber, Quantum Statistics of Superradiant Pulses, Phys. Rev. A 5,(1972)1457.
[52] Jun-Qi Li, Li-Bin Fu and J-Q Liang, Environment-induced disentanglement of the Einstein-Podolsky-Rosen system, J. Phys. B 41 (2008) 015504.
[53] Y. X. Liu, S. K. Ozdemir, M. Koashi, and N. Imoto, Dynamics of entanglement for coherent excitonic states in a system of two coupled quantum dots and cavity QED , Phys. Rev. A 65 (2002) 042326.
[54] L. Fu and J. Liu, Quantum entanglement manifestation of transition to nonlinear self-trapping for Bose-Einstein condensates in a symmetric double well, Phys. Rev. A 74 (2006) 063614.
[55] Y. D. Wang, P. Zhang, D. L. Zhou, and C. P. Sun, Fast entanglement of two charge-phase qubits through nonadiabatic coupling to a large Josephson junction, Phys. Rev. B 70 (2004) 224515.
[56] G. X. Li, Y. P.Yang, K. A.llaart, and D. Lenstra, Entanglement for excitons in two quantum dots in a cavity injected with squeezed vacuum, Phys. Rev. A 69 (2004) 014301.
[57] G. X. Li, H. T. Tan, S. P. Wu, and Y. P. Yang, Entanglement for excitons in two quantum dots placed in two separate single-mode cavities, Phys. Rev. A 70 (2004) 034307.
[58] Shao-Hua Xiang, Bin Shao et al., Revival and collapse of state preparation fidelity and multipartite entanglement in a coupled exciton-photon system, J. Phys. B 40, (2007)2351.
[59] S. Hameau, Y. Guldner et al., Strong Electron-Phonon Coupling Regime in Quantum Dots: Evidence for Everlasting Resonant Polarons, Phys. Rev. Lett. 83 (1999) 4152.
[60] L. Besombes, K. Kheng, L. Marsal and H. Mariette, Acoustic phonon broadening mechanism in single quantum dot emission, Phys. Rev. B 63 (2001) 155307.
[61] Ka-Di Zhu, Wai-Sang Li, Effect of quantum lattice fluctuations on quantum coherent oscillations in a coherently driven quantum dot-cavity system, Phys Lett A 314 (2003) 380.
[62] C.-H.Yuan, K. D. Zhu, and X. Z. Yuan, Exciton entanglement in coupled quantum dots in a microcavity, Phys. Rev. A 75 (2007) 062309.
[63] A. Joshi, B. Anderson, and M. Xiao, Violation of Bell's inequality for two coupled quantum dots confined in a cavity, Phys. Rev. B 75 (2007) 125304.
[64] J. M. Raimond, M. Brune, and S. Haroche, Manipulating quantum entanglement with atoms and photons in a cavity, Rev. Mod. Phys. 73 (2001) 565.
[65] Xiao-Zhong Yuan, Ka-Di Zhu, Wai-Sang Li, Influences of strong exciton-phonon interaction on two coupled quantum dots within cavity QED, Phys. Lett. A 329 (2004) 402.
[66] Fernando C. Lombardo, Paula I. Villar, Geometric phases in open systems: A model to study how they are corrected by decoherence, Phys Rev A 74 (2006) 042311.
[67] A. T. Rezakhani, P. Zanardi, Temperature effects on mixed-state geometric phase, Phys. Rev. A 73 (2006) 052117.
[68] X. Z.Yuan, H. S. Goan, K. D. Zhu, Non-Markovian reduced dynamics and entanglement evolution of two coupled spins in a quantum spin environment, Phys. Rev. B 75 (2007) 045331.
[69] M. Fujinaga, N. Hatano, The entanglement of the XY spin chain in a random magnetic field, Phys. Soc. Jpn. 76 (2007) 094001.
[70] M. Thorwart, P. Haggi, Decoherence and dissipation during a quantum xor gate operation, Phys. Rev. A 65 (2002) 012309.
[71] V. Turck, S. Rodt, et al., Effect of random field fluctuations on excitonic transitions of individual CdSe quantum dots, Phys. Rev. B 61 (2001) 9944.
[72] R. Heitz, I. Mukhametzhanov, et al., Enhanced Polar Exciton-LO-Phonon Interaction in Quantum Dots, Phys. Rev. Lett. 83 (1999) 4654.
[73] H. Kamda, H. Gotoh, et al., Emission of a Single Conjugated Polymer Chain Isolated in Its Single Crystal Monomer Matrix, Phys. Rev. Lett. 87 (2002) 087401.
[1]J.I.Cirac and P.Zoller,Preparation of macroscopic superpositions in many-atom systems, Phys. Rev. A 50 (1994) R2799.
[2] Shi-Biao Zheng, One-Step Synthesis of Multiatom Greenberger-Horne-Zeilinger States, Phys. Rev. Lett. 87 (2001) 230404.
[3] Shi-Biao Zheng, Generation of entangled states of multiple trapped ions in thermal motion, Phys. Rev. A 70 (2004) 045804.
[4] I. E. Linington and N. V. Vitanov, Robust creation of arbitrary-sized Dicke states of trapped ions by global addressing, Phys. Rev. A 77 (2008) 010302.
[5] W. X. Yang, Z. M. Zhan, and J. H. Li, Efficient scheme for multipartite entanglement and quantum information processing with trapped ions, Phys. Rev. A 72 (2005) 062108.
[6] J. A. Jones, M.Mosca, and R. H. Hansen, Implementation of a quantum search algorithm on a quantum computer, Nature (London) 393 (1998) 344.
[7] J. Q. You, J. S. Tsai, and Franco Nori, Controllable manipulation and entanglement of macroscopic quantum states in coupled charge qubits, Phys. Rev. B 68 (2003) 024510.
[8] F. Plastina, R. Fazio, and G. M. Palma, Macroscopic entanglement in Josephson nanocircuits, Phys. Rev. B 64 (2001)113306.
[9] L. F. Wei,Y. X. Liu, and F. Nori, Generation and Control of Greenberger-Horne-Zeilinger Entanglement in Superconducting Circuits, Phys. Rev. Lett. 96(2006)246803.
[10] L. F. Wei,Yu-xi Liu, M. J. Storcz, and F. Noril, Macroscopic Einstein-Podolsky-Rosen pairs in superconducting circuits, Phys. Rev. A 73 (2006) 052307.
[11] D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, Bell's theorem without inequalities, Am. J. Phys. 58, (1990) 1131.
[12] W. Dur, G. Vidal, and J. I. Cirac, Three qubits can be entangled in two inequivalent ways, Phys. Rev. A 62 (2000) 062314.
[13] M. Eib, N. Kiese, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, Experimental Realization of a Three-Qubit Entangled W State, Phys. Rev. Lett. 92 (2004) 077901.
[14] C. F. Roos, M. Riebe, H. Haffner, W. Hansel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, Control and Measurement of Three-Qubit Entangled States, Science 304 (2004) 1478.
[15] H. Mikami, Y. Li, K. Fukuoka, and T. Kobayashi, New High-Efficiency Source of a Three-Photon W State and its Full Characterization Using Quantum State Tomography, Phys. Rev. Lett. 95 (2005)150404.
[16] H. Haffner, W. Hansel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Korber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Guhne, W. Dur, and R. Blatt, Scalable multiparticle entanglement of trapped ions, Nature (London) 438 (2005) 643.
[17] R. Raussendorf and Hans J. Briegel, A One-Way Quantum Computer, Phys. Rev. Lett. 86(2001)5188.
[18] Hans J. Briegel and R. Raussendorf, Persistent Entanglement in Arrays of Interacting Particles, Phys. Rev. Lett. 86 (2001) 910.
[19] W. Dur and H. J. Briegel, Stability of Macroscopic Entanglement under Decoherence, Phys. Rev. Lett. 92 (2004) 180403.
[20] M. Borhani and D. Loss, Cluster states from Heisenberg interactions, Phys. Rev. A 71 (2005)034308.
[21] Shi-Biao Zheng, Generation of cluster states in ion-trap systems, Phys. Rev. A 73 (2006)065802.
[22] X. B. Zou, K. Pahlke, and W. Mathis, Quantum entanglement of four distant atoms trapped in different optical cavities, Phys. Rev. A 69 (2004) 052314.
[23] X. B. Zou and W. Mathis, Generating a four-photon polarization-entangled cluster state, Phys. Rev. A 71 (2005) 032308.
[24] X. B. Zou and W. Mathis, Schemes for generating the cluster states in microwave cavity QED, Phys. Rev. A 72 (2005) 013809.
[25] C. L. Jiang, M. F. Fang and Y. H. Hu , Efficient scheme of quantum SWAP gate and multi-atom cluster state via cavity QED, Chinese Physics B, 17 (2008)190.
[26] P. Dong, Zheng-Yuan Xue, M. Yang, and Zhuo-Liang Cao, Generation of cluster states, Phys. Rev. A 73 (2006) 033818.
[27] E. M. Becerra-Casto, W. B. Cardoso, A. T. Avelar, and B. Baseia, Generation of four-qubit cluster of entangled coherent states in bimodal QED cavities, e-print arXiv:quant-ph/0709.001 Ov1.
[28] J. Q. You, X. B. Wang, T. Tanamoto, and F. Nori, Efficient one-step generation of large cluster states with solid-state circuits, Phys. Rev. A 75 (2007) 052319.
[29] Z. Y. Xue and Z. D. Wang, Simple unconventional geometric scenario of one-way quantum computation with superconducting qubits inside a cavity, Phys. Rev. A 75 (2007)064303.
[30] Gang Chen, Zidong Chen, Lixian Yu, and Jiuqing Liang, One-step generation of cluster states in superconducting charge qubits coupled with a nanomechanical resonator, Phys. Rev. A 76 (2007) 024301.
[31] P. Walther, K. J. Resch, T. Rudolph, E. Schenk, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, Experimental one-way quantum computing, Nature (London) 434 (2005) 169. :
[32] N. Kiesel, C. Schmid, U. Weber, G. Toth, O. Guhne, R. Ursin, and H. Weinfurter, Experimental Analysis of a Four-Qubit Photon Cluster State, Phys. Rev. Lett. 95, (2005)210502.
[33] G. Vallone, E. Pomarico, P. Mataloni, F. De Martini, and V. Berardi, Realization and Characterization of a Two-Photon Four-Qubit Linear Cluster State, Phys. Rev. Lett. 98(2007)180502.
[34] M. Barbieri, C. Cinelli, F. De Martini, and P. Mataloni, Polarization-momentum hyperentangled states: Realization and characterization, Phys. Rev. A 72 (2005) 052110.
[35] S. B. Zheng and G. C. Guo, Efficient Scheme for Two-Atom Entanglement and Quantum Information Processing in Cavity QED, Phys. Rev. Lett. 85 (2000) 2392.
[36] S. Osnaghi, et al., Coherent Control of an Atomic Collision in a Cavity, Phys. Rev. Lett. 87 (2002) 037902.
[37] B .Yu, W. Z. Zhou, G. C. Guo, et al., Robust high-fidelity teleportation of an atomic state through the detection of cavity decay, Phys. Rev. A, 70 (2004) 014302.
[38] M. X. Lin, et al., Scheme for implementing quantum dense coding via cavity QED, Phys. Lett. A, 313 (2003) 351.
[39] P. Bertet et al., A complementarity experiment with an interferometer at the quantum-classical boundary, Nature (London) 411 (2001) 166.
[40] J. McKeever, et al., Deterministic generation of single photons from one atom trapped in a cavity, Science 303 (2004) 1992.
[41] P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinlcse, and G. Rempe, Cavity cooling of a single atom, Nature 428 (2004) 50.
[42] G. R. Guthohrlein, A single ion as a nanoscopic probe of an optical field, Nature 414 (2001)49.
[43] E. Solano, G. S. Agarwal, and H. Walther, Strong-Driving-Assisted Multipartite Entanglement in Cavity QED, Phys. Rev. Lett. 90 (2003) 027903.
[44] S. B. Zheng, Quantum-information processing and multiatom-entanglement engineering with a thermal cavity, Phys. Rev. A 66 (2002) 060303(R).
[45] Liu Ye, Long-Bao Yu, and Guang-Can Guo, Generation of entangled states in cavity QED, Phys. Rev. A 72 (2005) 034304 (also seen the erratum: Phys. Rev. A 73 (2006) 029907(E)).
[46] M. Bina, F. Casagrande, A. Lulli, and E. Solano, Monitoring atom-atom entanglement and decoherence in a solvable tripartite open system in cavity QED, Phys. Rev. A 77 (2008) 033839.
[47] P. Lougovski,E. Solano, and H. Walther, Generation and purification of maximally entangled atomic states in optical cavities, Phys. Rev. A 71 (2005) 013811.
[48] Jun-Qi Li, Gang Chen, and J.-Q. Liang, One-step generation of cluster states in microwave cavity QED, Phys. Rev. A 77 (2008) 014304.
[49] C.-Y. Chen and M. Feng, Suppression of the heating effect in a geometric logic gating in a strong-driving-assisted cavity QED scheme, Physical Review A 77 (2008) 012325.
[50] Xun-Li Feng, Zisheng Wang, Chunfeng Wu, L. C. Kwek, C. H. Lai, and C. H. Oh, Scheme for unconventional geometric quantum computation in cavity QED, Physical Review A 75 (2007) 052312.
[51] Yong Li, Li Zheng, Yu-xi Liu, and C. P. Sun, Correlated photons and collective excitations of a cyclic atomic ensemble, Physical Review A 73 (2006) 043805.
[52] C.Y. Chen, M. Feng, X. L. Zhang, and K. L. Gao, Strong-driving-assisted unconventional geometric logic gate in cavity QED, Phys. Rev. A 73 (2006) 032344.
[53] C.Y.Chen, M. Feng, and K. L.Gao, Superposition and entanglement of mesoscopic squeezed vacuum states in cavity QED, Phys. Rev.A 73 (2006) 034305.
[2]A.Yao,In Procedings of the 34th Annual Symposium of Foundation of Computer Science(1993) 352.
[3]A.Barenco,C.H.Bennett,R.Cleve,D.P.DiVincenzo,N.Margolus,P.Shor,et al.,Elementary gates for quantum computation,Phys.Rev.A 52(1995) 3457.
[4]C.Monroe,D.M.Meekhof,B.E.King,et al.,Demonstration of a Fundamental Quantum Logic Gate,Phys.Rev.Lett.75(1995) 4714.
[5]A.Rauschenbeutel,G.Nogues,S.Osnaghi,P.Bertet,M.Brune,J.M.Raimond,and S.Haroche,Coherent Operation of a Tunable Quantum Phase Gate in Cavity QED,Phys.Rev.Lett.83(1999) 5166.
[6]J.K.Pathos and P.L.Knight,Quantum Computation with a One-Dimensional Optical Lattice,Phys.Rev.Lett.91(2003) 107902.
[7]H.Ollivier and P.Milman,Proposal for realization ofa Toffoli gate via cavity-assisted collision,e-print quant-ph/0306064.
[8]J.Zhang,W.Liu,Z.Deng,Z.Lu,and G.L.Long,Modularization of a multi-qubit controlled phase gate and its nuclear magnetic resonance implementation,J.Opt.B 7(2005) 22.
[9]C.P.Yang and S.Han,n-qubit-controlled phase gate with superconducting quantum-interference devices coupled to a resonator,Phys.Rev.A 72(2005) 032311.
[10]X.B.Zou,K.Li,and G.C.Guo,Linear optical scheme for direct implementation of a nondestructive N-qubit controlled phase gate,Phys.Rev.A 74(2006) 044305.
[11]C.H.Bennett,G.Brassard,C.Crepeau,R.Jozsa,A.Peres,and W.K.Wootters,Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,Phys.Rev.Lett.70(1993)1895.
[12]D.Bouwmeester,J.W.Pan,K.Mattle,M.Eibl,H.Weinfurter,A.Zeilinger,Experimental quantum teleportation,Nature 390(1998) 575.
[13]D.Boschi,S.Branca,F.De Martini,L.Hardy,and S.Popescu,Experimental Realization of Teleporting an Unknown Pure Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels,Phys.Rev.Lett.80(1998) 1121.
[14]A.Furusawa,J.L.Sorensen,S.L.Braunstein,C.A.Fuchs,H.J.Kimble,E.S.Polzik,Unconditional quantum teleportation,Science 282(1998) 706.
[15]Yu.A.Chen,S.Chen,Z.S.Yuan,B.Zhao,C.S.Chuu,J.Schmiedmayer,J.W.Pan,Memory-built-in quantum teleportation with photonic and atomic qubits,Nature Physics 4(2008)103.
[16]W.H.Zurek,Pointer basis of quantum apparatus:Into what mixture dose the wave packet collapse,Phys.Rev.D,24(1981) 1516.
[17]W.H.Zurek,Envionment-induced superselection rules,Phys.Rev.D,26(1982)1862.
[18]R.Kubo,Note on the stochastic theory of resonance absorption,J.Phys.Soc.Jap.9,(1954) 935.
[19]G.J.Milburn,Intrinsic decoherence in quantum mechanics,Phys.Rev.A 44(1991)5401.
[20]H.D.Zeh,Found Phys,1(1970) 69.
[21]曾谨言,裴寿镛主编.量子力学新进展[M]:第一辑.北京:北京大学出版社,2000,59-127.
[22]P.Zhang,X.F.Liu,C.P.Sun Consisitent approach for quantum measurement,Phys.Rev.A 66(2002) 042104.
[23]C.J.Myatt,B.Q.King,A.Turchette et al.,Nature,403(2000) 269.
[24]P.W.Anderson,A Mathematical Model for the Narrowing of Spectral Lines by Exchange or Motion,J.Phys.Soc.Jap 9(1954) 316.
[25]V.Buzek and M.Konopka,Dynamics of open systems governed by the Milburn equation,Phys.Rev.A 58(1998) 1735.
[26] M. Schlosshauer, Self-induced decoherence approach: Strong limitations on its validity in a simple spin bath model and on its general physical relevance, Phys. Rev. A 72 (2005)012109.
[27] Renato M. Angelo, E. S. Cardoso and K. Furuya, Decoherence induced by a phase-damping reservoir, Phys. Rev. A 73 (2006) 062107.
[28] Xian-Ting Liang, Non-Markovian dynamics and phonon decoherence of a double quantum dot charge qubit, Phys. Rev. B 72 (2005) 245328.
[29] Michael Thorwart and Peter Hanggi, Decoherence and dissipation during a quantum XOR gate operation, Phys. Rev. A 65 (2002) 012309.
[30] Pochung Chen, Dynamical decoupling-induced renormalization of non-Markovian dynamics, Phys. Rev. A 75 (2007) 062301.
[31] Adrian A. Budini, Random Lindblad equations from complex environments, Phys. Rev. E 72 (2007) 056106.
[32] S. Maniscalco, Complete positivity of a spin-112 master equation with memory, Phys. Rev. A 75 (2007) 062103.
[33] D. F. Walls and G J. Milburn, Effect of dissipation on quantum coherence, Phys. Rev. A 31 (1985)2403.
[34] D. N(?)ller, L. B. Madsen, and K. Malmer, Geometric phases in open tripod systems, Phys. Rev. A 77 (2008) 022306.
[35] Gregory A. Fiete and Eric J. Heller, Semiclassical theory of coherence and decoherence, Phys. Rev. A 68 (2003) 022112.
[36] J. I. Kim, M. C. Nemes, A. F. de Toledo Piza, and H. E. Borges, Perturbative Expansion for Coherence Loss, Phys. Rev. Lett. 77 (1996) 207.
[37] C. W. Gardiner, P. Zoller, Quantum Noise, 2000, Springer-Verlag, Berlin.
[38] W.G Unruh, Experimental Study of High-Beta Tokamak Stability, Phys. Rev. A 51, (1995)992.
[39] O. Astafiev, Yu. A. Pashkin, Y. Nakamura, T. Yamamoto, and J. S. Tsai, Quantum Noise in the Josephson Charge Qubit, Phys. Rev. Lett. 93 (2004) 267007.
[40] S. Vorojtsov, E. R. Mucciolo, and Harold U. Baranger, Phonon decoherence of a double quantum dot charge qubit, Phys. Rev. B 71 (2005) 205322.
[41] T. Hayashi, T. Fujisawa, H. D. Cheong, Y. H. Jeong, and Y. Hirayama, Coherent Manipulation of Electronic States in a Double Quantum Dot, Phys. Rev. Lett. 91 (2003)226804; J. R. Petta, A. C. Johnson, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Manipulation of a Single Charge in a Double Quantum Dot, Phys. Rev. Lett. 93 (2004) 186802.
[42] M. Thorwart, J. Eckel, and E. R. Mucciolo. Non-Markovian dynamics of double quantum dot charge qubits due to acoustic phonons, Phys. Rev. B 72 (2005) 235320.
[43] D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, et al., Experimental issues in coherent quantum-state manipulation of trapped atomic ions, J. Res. Natl Inst. Stand. Tech. 103 (1998) 259.
[44] A. M. Steane, Error Correcting Codes in Quantum Theory, Phys. Rev. Lett. 77(1996) 793.
[45] A. R. Calderbank and Peter W. Shor, Good quantum error-correcting codes exist, Phys. Rev. A 54 (1996) 1098.
[46] Lev Ioffe and Marc Mezard, Asymmetric quantum error-correcting codes, Phys. Rev. A 75 (2007)032345.
[47] Lu-Ming Duan and Guang-Can Guo, Preserving Coherence in Quantum Computation by Pairing Quantum Bits, Phys. Rev. Lett. 79 (1997) 1953.
[48] H. Wei, Z. J. Deng,. X. L. Zhang, and M. Feng, Transfer and teleportation of quantum states encoded in decoherence-free subspace, Phys. Rev. A 76 (2007) 054304.
[49] L. Viola and S. Lloyd, Dynamical suppression of decoherence in two-state quantum systems, Phys. Rev. A 58 (1998) 2733.
[50] J. Bergli and L. Faoro, Exact solution for the dynamical decoupling of a qubit with telegraph noise, Phys. Rev. B 75 (2007) 054515.
[51] K. Shiokawa and D. A. Lidar, Dynamical decoupling using slow pulses: Efficient suppression of 1/f noise, Phys. Rev. A 69 (2004) 030302.
[52] D. A. Lidar, D. Bacon, and K. B. Whaley, Concatenating Decoherence-Free Subspaces with Quantum Error Correcting Codes, Phys. Rev. Lett. 82 (1999) 4556.
[53]M.S.Byrd,D.A.Lidar,L.A.Wu,and P.Zanardi,Universal leakage elimination,Phys.Rev.A 71(2005) 052301.
[54]Y.Zhang,Z.W.Zhou,B.Yu,and G.C.Guo,Concatenating dynamical decoupling with decoherence-free subspaces for quantum computation,Phys.Rev.A 69(2004)042315.
[55]A.Einstein,B.Podolsky,N.Rosen,Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Phys.Rev.47(1935) 777.
[56]Schr(o|¨)dinger,Naturwissenschaften,23(1935) 807.
[57]D.Bohm,量子理论,侯得彭译,北京,商务印书馆,1982.
[58]J.S.Bell,Physics 1(1964)195.
[59]A.Aspect,P.Grangier,and G.Roger,Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment:A New Violation of Bell's Inequalities,Phys.Rev.Lett.49(1982) 91.
[60]A.Aspect,J.Dalibard,and G.Roger,Experimental Test of Bell's Inequalities Using Time- Varying Analyzers,Phys.Rev.Lett.49(1982) 1804.
[61]M.A.Nielsen,I.L.Chuang,Quantum Computation and Quantum InformationCambridge University Press,Cambridge,(2000).
[62]李承祖等,量子通信与量子计算,长沙:国防科技大学出版社,2000:8.
[63]V.Vedarl,et al.,Quantifying Entanglement,Phys.Rev.Lett.78(1997) 2275.
[64]M.Horodecki,P.Horodecki,R.Horodecki,Separability of mixed quantum states:linear contractions approach,Open Syst.Inf.Dyn.13(2006) 103.
[65]W.K.Wootters,Entanglement of Formation of an Arbitrary State of Two Qubits,Phys.Rev.Lett.80(1998) 2245.
[66]P.Rungtal,V.Buzek,C.M.Caves,M.Hiilery,and G.J.Milbum,Universal state inversion and concurrence in arbitrary dimensions,Phys.Rev.A 64(2001) 042315.
[67]S.Albeverio,and S.M.Fei,A note on invariants and entanglements,J.Opt.B 3(2001) 223.
[68]A.Peres,Separability Criterion for Density Matrices,Phys.Rev.Lett.77(1996) 1413.
[69]G.Vidal and R.F.Werner,Computable measure of entanglement,Phys.Rev.A 65 (2002)032314.
[70] T. Wei and P. Goldbart, Geometric measure of entanglement and applications to bipartite and multipartite quantum states, Phys. Rev. A 68 (2003) 042307.
[71] T. Wei, M. Ericsson, P. Goldbart and W. Munro, Quant. Inf. Comput. 4 (2004) 252.
[72] D. A. Meyer, and N. R. Wallach, J. Math. Phys, 43 (2002) 4273.
[73] F. Verstraete, M. Popp, and J. I. Cirac, Entanglement versus Correlations in Spin Systems, Phys. Rev. Lett. 92 (2004) 027901.
[74] D. M. Greenberger, M. A. Home, A. Shimony, and A. Zeilinger, Bell theorem without inequalities, Am. J. Phys. 58 (1990) 1131.
[75] W. Dur, G. Vidal, and J. 1. Cirac, Three qubits can be entangled in two inequivalent ways, Phys. Rev. A 62 (2000) 062314.
[76] R. F. Werner, Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model, Phys. Rev. A 40 (1989) 4277.
[77] C. H. Bennett, G. Brassard, S. Popescu, et al., Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels, Phys. Rev. Lett. 76 (1996) 722.
[78] H. J. Briegel and R. Raussendorf, Persistent Entanglement in Arrays of Interacting Particles, Phys. Rev. Lett. 86 (2001) 910.
[79] C. Sackett, D. Kielpinski, B. King, et al., Experimental entanglement of four particles, Nature (London) 404 (2000) 256.
[80] A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J. Raimond, and S. Haroche, Step-by-Step Engineered Multiparticle Entanglement, Science, 288 (2000) 2024.
[81] I. L. Chuang, N. Gershenfeld, and M. Kubinec, Experimental Implementation of Fast Quantum Searching, Phys. Rev. Lett. 80 (1998) 3408.
[82] E. Knill, R. Laflamme, R. Martinez, C.-H. Tseng, An algorithmic benchmark for quantum information processing, Nature (London) 404 (2000) 368.
[83] D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, Observation of Three-Photon Greenberger-Horne-Zeilinger Entanglement, Phys. Rev. Lett. 82 (1999) 1345.
[84] M. G. Moore and P. Meystre, Generating Entangled Atom-Photon Pairs from Bose-Einstein Condensates, Phys. Rev. Lett. 85 (2000) 5026.
[85] A. S0rensen, L.-M. Duan, J. I. Cirac, P. Zoller, Many-particle entanglement with Bose-Einstein condensates, Nature (London) 409 (2001) 63.
[86] P. K. Day, H. G. LeDuc, B. A. Mazin, A. Vayonakis and J. Zmuidzinas, A broadband superconducting detector suitable for use in large arrays, Nature (London) 425 (2003) 817.
[1]M.A.Nielsen,I.L.Chuang,Quantum Computation and Quantum Information,Cambridge University Press,Cambridge,2000.
[2]R.Raussendorfand Hans J.Briegel,A One-Way Quantum Computer,Phys.Rev.Lett.86(2001) 5188.
[3]P.Walther,K.J.Resch,T.Rudolph,E.Schenk,H.Weinfurter,V.Vedral,M.Aspelmeyer,and A.Zeilinger,Experimental one-way quantum computing,Nature (London) 434 (2005)169.
[4] N. Kiesel, C. Schmid, U. Weber, G. Toth, O. Guhne, R. Ursin, and H. Weinfurter, Experimental Analysis of a Four-Qubit Photon Cluster State, Phys. Rev. Lett. 95 (2005)210502.
[5] G. Vallone, E. Pomarico, P. Mataloni, F. De Martini, and V. Berardi, Realization and Characterization of a Two-Photon Four-Qubit Linear Cluster State, Phys. Rev. Lett. 98(2007)180502.
[6] M. S. Tame, R. Prevede, M. Paternostro, P. Bohi, M. S. Kim, and A. Zeilinger, Experimental Realization of Deutsch's Algorithm in a One-Way Quantum Computer, Phys. Rev. Lett. 98 (2007) 140501.
[7] S. Das, R. Kobes, and G. Kunstatter, Adiabatic quantum computation and Deutsch's algorithm, Phys. Rev. A 65 (2002) 062310.
[8] A. M. Childs, E. Farhi, and J. Preskill, Robustness of adiabatic quantum computation, Phys. Rev. A 65 (2002) 012322.
[9] D. P. Divincenzo, Quantum Computation, Science 270 (1995) 255; Two-bit gates are universal for quantum computation, Phys. Rev. A 51 (1995) 1015.
[10] A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, Elementary gates for quantum computation, Phys. Rev. A 52 (1995) 3457.
[11] D. DiVincenzo, "The physical implementation of quantum computation," Fortschr. Phys. 48 (2000) 771.
[12] DiVincenzo, D., 1997, in Mesoscopic Electron Transport, edited by L. Kouwenhoven, G. Schon, and L. Sohn, NATO AST Series E: Applied Sciences No. 345 (Kluwer Academic, Dordrecht), p. 657.
[13] T. P. Orlando, J. E. Mooij, Lin Tian, Caspar H. van der Wal, L. S. Levitov, Seth Lloyd, and J. J. Mazo, Superconducting persistent-current qubit, Phys. Rev. B 60, (1999) 15398.
[14] M. Grajcar, A. Izmalkov, S. H. van der Ploeg, S. Linzen, T. Plecenik, Th. Wagner, et al, Four-Qubit Device with Mixed Couplings, Phys. Rev. Lett. 96 (2006) 047006.
[15] L. F. Wei, J. R. Johansson, L. X. Cen, S. Ashhab, and Franco Nori, Controllable Coherent Population Transfers in Superconducting Qubits for Quantum Computing, Phys. Rev. Lett. 100 (2008) 113601.
[16] Y. Nakamura, Yu. A. Pashkin, and J. S. Tsai, Coherent control of macroscopic quantum states in a singleCooper-pair box, Nature (London), 398 (1999) 786.
[17] T. Yamamoto, Yu.A. Pashkin, O. Astafiev, Y. Nakamura and J.S. Tsai, Demonstration of conditional gate operation using superconducting charge qubits, Nature 425 (2003) 941.
[18] G. Burkard, D. Loss, and D. P. DiVincenzo, Coupled quantum dots as quantum gates, Phys. Rev. B 59 (1999) 2070.
[19] T. Tanamoto, Quantum gates by coupled asymmetric quantum dots and controlled-NOT-gate operation, Phys. Rev. A 61 (2000) 022305.
[20] T. Sleator and H. Weinfurter, Realizable Universal Quantum Logic Gates, Phys. Rev. Lett. 74 (1995) 4087.
[21] Y. F. Xiao, X. M. Lin, J. Gao, Y. Yang, Z. F. Han, and G.-C. Guo, Realizing quantum controlled phase flip through cavity QED, Phys. Rev. A 70 (2004) 042314.
[22] V. Giovannetti, D. Vitali, P. Tombesi, and A. Ekert, Scalable quantum computation with cavity QED systems, Phys. Rev. A 62 (2000) 032306.
[23] M. C. de Oliveira and W. J. Munro, Quantum computation with mesoscopic superposition states, Phys. Rev. A 61 (2000) 042309.
[24] L. M. K. Vandersypen and I. L. Chuang, NMR techniques for quantum control and computation, Rev. Mod. Phys. 76 (2004)1037.
[25] L. M. Vandersypen, M. Steffen, G. Breyta, C. S. Yannoni, R. Cleve, and I. L. Chuang, Experimental Realization of an Order-Finding Algorithm with an NMR Quantum Computer, Phys. Rev. Lett. 85 (2000) 5452.
[26] A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J. M. Raimond, and S. Haroche, Coherent Operation of a Tunable Quantum Phase Gate in Cavity QED, Phys. Rev. Lett. 83 (1999) 5166.
[27] G. W. Lin, X. B. Zou, M.-Y. Ye, X.-M. Lin, and G.-C. Guo, Scheme for tunable quantum phase gate and effective preparation of graph-state entanglement, Phys. Rev. A 77 (2008)032308.
[28] Z. J. Deng, X. L. Zhang, H. Wei, K. L. Gao, and M. Feng, Implementation of a nonlocal N -qubit conditional phase gate by single-photon interference, Phys. Rev. A 76 (2007) 044305.
[29] S. B. Zheng and G.-C. Guo, Efficient Scheme for Two-Atom Entanglement and Quantum Information Processing in Cavity QED, Phys. Rev. Lett. 85 (2000) 2392.
[30] O. Zilberberg, B. Braunecker, and D. Loss, Controlled-NOT gate for multiparticle qubits and topological quantum computation based on parity measurements, Phys.Rev.A 77 (2008) 012327.
[31] N. Sangouard, X. Lacour, S. Guerin, and H. R. Jauslin, Fast SWAP gate by adiabatic passage, Phys. Rev. A 72 (2005) 062309.
[32] B. Wang and L.-M. Duan, Implementation scheme of controlled SWAP gates for quantum fingerprinting and photonic quantum computation, Phys. Rev. A 75 (2007) 050304.
[33] M. Thorwart and P. Hanggi, Decoherence and dissipation during a quantum XOR gate operation, Phys. Rev. A 65 (2002) 012309.
[34] Markus J. Storcz and Frank K. Wilhelm, Decoherence and gate performance of coupled solid-state qubits, Phys. Rev. A 67 (2003) 042319.
[35] C. D. Hilll, and H. S.Goan, Gates for the Kane quantum computer in the presence of dephasing, Phys. Rev. A 70 (2003) 022310.
[36] E. Charron, E. Tiesinga, F. Mies, and C. Williams, Optimizing a Phase Gate Using Quantum Interference, Phys.Rev.Lett. 88 (2002) 077901.
[37] H. Wei, Z. J. Deng, X. L. Zhang, and M. Feng, Transfer and teleportation of quantum states encoded in decoherence-free subspace, Phys. Rev. A 76 (2007) 054304.
[38] Shi-Biao Zheng, Quantum-information processing and multiatom-entanglement engineering with a thermal cavity, Phys. Rev. A 66, 060303 (2002).
[39] Y. Makhlin, G. Schon, A. Shnirman, Quantum-state engineering with Josephson-junction devices, Rev. Mod. Phys. 73 (2001) 357.
[40] J. I. Cirac, P. Zoller, Quantum Computations with Cold Trapped Ions, Phys. Rev. Lett. 74(1995)4091.
[41] Y. C. Cheng, R. Silbey, Stochastic Liouville equation approach for the effect of noise in quantum computations, Phys. Rev. A 69 (2004) 052325.
[42] C. P. Sun, H. Zhan, and X. F. Liu, Decoherence and relevant universality in quantum algorithms via a dynamic theory for quantum measurement, Phys. Rev. A 58 (1998) 1810.
[43] A. Fedorov, L. Fedichkin, V. Privman, Evaluation of Decoherence for Quantum Control and Computing, J. Comp. Theor. Nanosci. 1, 132 (2004); L. Fedichkin, A. Fedorov, V. Privman, Measures of Decoherence, Proc. SP1E 5105 (2003) 243.
[44] I. L. Chuang, N.A. Gershenfeld, M. Kubinec, Experimental Implementation of Fast Quantum Searching, Phys. Rev. Lett. 80 (1998) 3408.
[45] E. Knill, R. Laflamme, R. Martinez, C.-H. Tseng, An algorithmic benchmark for quantum information processing, Nature 404 (2000) 368.
[46] T. Pellizzari, S.A. Gardiner, J.I. Cirac, P. Zoller, Decoherence, Continuous Observation, and Quantum Computing: A Cavity QED Model, Phys. Rev. Lett. 75 (1995)3788.
[47] D. Loss, D.P. Divincenzo, Quantum computation with quantum dots, Phys. Rev. A 57 (1998)120.
[48] K. Kimm, H. wang-h. Kwon, Decoherence of the quantum gate in Milburn's model of decoherence, Phys. Rev. A 65 (2002) 022311.
[49] D. Ahn, J.H. Oh, K. Kimm, S.W. Hwang, Time-convolutionless reduced-density-operator theory of a noisy quantum channel: Two-bit quantum gate for quantum-information processing, Phys. Rev. A 61 (2000) 052310.
[50] J. F. Poyatos, J. I. Cirac, P. Zoller, Complete Characterization of a Quantum Process: The Two-Bit Quantum Gate, Phys. Rev. Lett. 78 (1997) 390.
[51] X. T. Liang, Short-time decoherence of Josephson charge qubits, Phys. B 362 (2005) 243.
[52] D.Tolkunov, V.Privman, Short-time decoherence for general system-environment interactions, Phys. Rev. A 69 (2004) 062309.
[53] L. Viola, S. Lloyd, Dynamical suppression of decoherence in two-state quantum systems, Phys. Rev. A 58 (1998) 2733.
[54] G. Massimo Palma, K.-A. Suominen, A.K. Ekert, Quantum computation and dissipation, Proc. R. Soc. Lond. A 452 (1996) 567.
[55] L. Fedichkin, A. Fedorov, Error rate of a charge qubit coupled to an acoustic phonon reservoir, Phys. Rev. A 69 (2004) 032311.
[1]M.Schlosshauer,Decoherence,the measurement problem,and interpretations of quantum mechanics,Rev.Mod.Phys.76(2005)1267.
[2]张永德,量子信息物理原理,科学出版社,2006.
[3]D.Braun,Creation of Entanglement by Interaction with a Common Heat Bath,Phys.Rev.Lett.89(2002) 277901.
[4]F.Benatti,R.Floreanini and M.Piani,Environment Induced Entanglement in Markovian Dissipative Dynamics,Phys.Rev.Lett.91(2003) 070402.
[5]A.Hutton and S.Bose,Mediated entanglement and correlations in a star network of interacting spins,Phys.Rev.A 69(2004) 042312.
[6]Y.Hamdouni,M.Fannes,and F.Petruccione,Exact dynamics of a two-qubit system in a spin star environment,Phys.Rev.B 73(2006) 245323.
[7]Xiao-Zhong Yuan,Hsi-Sheng Goan,and Ka-Di Zhu,Non-Markovian reduced dynamics and entanglement evolution of two coupled spins in a quantum spin environment, Phys. Rev. B 75 (2007) 045331.
[8] M. A. Nielsen, I. L. Chuang, Quantum Computation and Quantum Information, Cambridge Univ. Press, 2000.
[9] C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels, Phys. Rev. Lett. 70 (1993) 1895; G. Rigolin, Quantum teleportation of an arbitrary two-qubit state and its relation to multipartite entanglement, Phys. Rev. A 71 (2005) 032303.
[10] C. H. Bennett, S. J. Wiesner, Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states, Phys. Rev. Lett. 69 (1992) 2881.
[11] A. K. Ekert, Quantum cryptography based on Bell's theorem, Phys. Rev. Lett. 67 (1991)661; M. Curty, M. Lewenstein, N. Lukenhaus, Entanglement as a Precondition for Secure Quantum Key Distribution, Phys. Rev. Lett. 92 (2004) 217903; K. Inoue, C. Santori, E. Waks, Y. Yamamoto, Entanglement-based quantum key distribution without an entangled-photon source, Phys. Rev. A 67 (2003) 062319.
[12] C. H. Bennett, H. J. Bernstein, S. Popescu, B. Schumacher, Concentrating partial entanglement by local operations, Phys. Rev. A 53 (1996) 2046.
[13] A. Peres, Quantum Theory: Concepts and Methods, Kluwer Academic, Boston, 1995.
[14] T. Yu, J. H. Eberly, Phonon decoherence of quantum entanglement: Robust and fragile states, Phys. Rev. B 66 (2002) 193306;
[15] T. Yu, J. H. Eberly, Qubit disentanglement and decoherence via dephasing, Phys. Rev. B 68 (2003)165322;
[16] T. Yu, J. H. Eberly, Finite-Time Disentanglement Via Spontaneous Emission, Phys. Rev. Lett. 93 (2004) 140404.
[17] V. Privman, D. Tolkunov, Decoherence and loss of entanglement, Proceeding of SPIE 5815 (2005)187; D. Tolkunov, V. Privman, P. K. Aravind, Decoherence of a measure of entanglement, Phys. Rev. A 71 (2005) 060308.
[18] K. Roszak, P. Machnikowski, Complete disentanglement by partial pure dephasing,Phys. Rev. A 73 (2006) 022313; A. Jamroz, Local aspects of disentanglement induced by spontaneous emission, quant-ph/0602128.
[19] R. Andre, R. Carvalho, F. Mintert, S. Palzer, A. Buchleitner, Entanglement dynamics under decoherence: from qubits to qudits, quant-ph/0508114.
[20] T. Yu, J. H. Eberly, Sudden Death of Entanglement: Classical Noise Effects, Opt. Commun. 264 (2006) 393.
[21] M. Yonac, T. Yu, J. H. Eberly, Sudden Death of Entanglement of Two Jaynes-Cummings Atoms, J. Phys. B 39 (2006) 621
[22] C. Pineda, T. H. Seligman, Evolution of pairwise entanglement in a coupled n-body system,Phys. Rev. A 73 (2006) 012305.
[23] X.-T. Liang, Initial decoherence and disentanglement of open two-qubit systems,Phys. Lett. A 349 (2006) 98.
[24] Asma Al-Qasimi and Daniel F. V. James, Sudden death of entanglement at finite temperature, Phys. Rev. A 77 (2008) 012117.
[25] Manzoor Ikram, Fu-li Li, and M. Suhail Zubairy, Disentanglement in a two-qubit system subjected to dissipation environments, Phys. Rev. A 75 (2007) 062336.
[26] Xiufeng Cao and Hang Zheng, Non-Markovian disentanglement dynamics of a two-qubit system, Phys. Rev. A 77 (2008) 022320.
[27] B. Bellomo, R. Lo Franco, and G. Compagno, Non-Markovian Effects on the Dynamics of Entanglement, Phys. Rev. Lett, 99 (2007) 160502.
[28] M. Yonac, T. Yu, J. H. Eberly, Sudden Death of Entanglement of Two Jaynes-Cummings Atoms, J. Phys. B 39 (2006) 621
[29] Zhi-Jian Li, Jun-Qi Li, Yan-Hong Jin and Yi-Hang Nie, Time evolution and transfer of entanglement between an isolated atom and a Jaynes-Cummings atom, J. Phys. B, 40 (2007) 3401.
[30] Ru-Fen Liu and Chia-Chu Chen, Role of the Bell singlet state in the suppression of disentanglement, Phys. Rev. A 74 (2006) 024102.
[31] T. Yu and J. H. Eberly, Quantum Open System Theory: Bipartite Aspects, Phys.Rev. Lett 97 (2006) 140403.
[32] M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, L. Davidovich, Environment-Induced Sudden Death of Entanglement, Science, 316(2007)579.
[33] A. R. P. Rau, Mazhar Ali, G. Alber, Hastening, delaying, or averting sudden death of quantum entanglement, EPL, 82 (2008) 40002.
[34] Marcelo O Terra Cunha, The geometry of entanglement sudden death, New Journal of Physics 9 (2007) 237.
[35] Ting Yu, Entanglement decay versus energy change: A model, Physics Letters A 361 (2007) 287.
[36] H. T. Cui , K. Li, X.X. Yi, A study on the sudden death of entanglement, Physics Letters A 365 (2007) 44.
[37] L. Aolita, R. Chaves, D. Cavalcanti, A. Aci n, and L. Davidovich, Scaling Laws for the Decay of Multiqubit Entanglement, Phys. Rev. Lett. 100 (2008) 080501.
[38] X. Q. Su, A. M. Wang, X. S. Ma and L. Qiu, Entanglement sudden death in a spinchannel, J. Phys. A 40 (2007) 11385.
[39] Z. Sun and X. G. Wang, Disentanglement in a quantum-critical environment, Phys. Rev. A 75 (2007) 062312.
[40] X. S. Ma, An M. Wang, and Y. Cao, Entanglement evolution of three-qubit states in a quantum-critical environment, Phys. Rev. B 76 (2007) 155327.
[41] Jun-Qi Li, Zhi-Jian Li, C. Gang, J.-Q. Liang, Time-evolving disentanglement in a spin-boson model, Physics Letters A 359 (2006) 275.
[42] W. K. Wootters, Entanglement of Formation of an Arbitrary State of Two Qubits, Phys. Rev. Lett. 80 (1998) 2245.
[43] C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, W. K. Wootters, Mixed-state entanglement and quantum error correction, Phys. Rev. A 54 (1996) 3824.
[44] V. Vedral, M. B. Plenio, M. A. Rippin, P.L. Knight, Quantifying Entanglement, Phys. Rev. Lett. 78 (1997) 2275.
[45] A. Peres, parability Criterion for Density Matrices, Phys. Rev. Lett. 77 (1996) 1413; K. Zyczkowski, P. Horodecki, A. Sanpera, M. Lewenstein, Volume of the set of separable states, Phys. Rev. A 58 (1998) 883.
[46] G. Lagmago Kamta, A.F. Starace, Anisotropy and Magnetic Field Effects on the Entanglement of a Two Qubit Heisenberg XY Chain, Phys. Rev. Lett. 88 (2002) 107901.
[47] R. Werner, Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model, Phys. Rev. A 40 (1989) 4277.
[48] R. Horodecki, M. Horodecki, Information-theoretic aspects of inseparability of mixed states, Phys. Rev. A 54 (1996) 1838.
[49] H. J. Carmichael, Statistical methods in quantum optics Master Equations and Fokker-Planck Equations (Berlin: Springer) (1999) pp 232-3.
[50] J. S. Pratt, Universality in the Entanglement Structure of Ferromagnets, Phys. Rev. Lett. 93 (2004) 237205.
[51] R. H. Dicke, Coherence in Spontaneous Radiation Processes, Phys. Rev. 93 (1954) 99; F. Haake and R. J. Glauber, Quantum Statistics of Superradiant Pulses, Phys. Rev. A 5,(1972)1457.
[52] Jun-Qi Li, Li-Bin Fu and J-Q Liang, Environment-induced disentanglement of the Einstein-Podolsky-Rosen system, J. Phys. B 41 (2008) 015504.
[53] Y. X. Liu, S. K. Ozdemir, M. Koashi, and N. Imoto, Dynamics of entanglement for coherent excitonic states in a system of two coupled quantum dots and cavity QED , Phys. Rev. A 65 (2002) 042326.
[54] L. Fu and J. Liu, Quantum entanglement manifestation of transition to nonlinear self-trapping for Bose-Einstein condensates in a symmetric double well, Phys. Rev. A 74 (2006) 063614.
[55] Y. D. Wang, P. Zhang, D. L. Zhou, and C. P. Sun, Fast entanglement of two charge-phase qubits through nonadiabatic coupling to a large Josephson junction, Phys. Rev. B 70 (2004) 224515.
[56] G. X. Li, Y. P.Yang, K. A.llaart, and D. Lenstra, Entanglement for excitons in two quantum dots in a cavity injected with squeezed vacuum, Phys. Rev. A 69 (2004) 014301.
[57] G. X. Li, H. T. Tan, S. P. Wu, and Y. P. Yang, Entanglement for excitons in two quantum dots placed in two separate single-mode cavities, Phys. Rev. A 70 (2004) 034307.
[58] Shao-Hua Xiang, Bin Shao et al., Revival and collapse of state preparation fidelity and multipartite entanglement in a coupled exciton-photon system, J. Phys. B 40, (2007)2351.
[59] S. Hameau, Y. Guldner et al., Strong Electron-Phonon Coupling Regime in Quantum Dots: Evidence for Everlasting Resonant Polarons, Phys. Rev. Lett. 83 (1999) 4152.
[60] L. Besombes, K. Kheng, L. Marsal and H. Mariette, Acoustic phonon broadening mechanism in single quantum dot emission, Phys. Rev. B 63 (2001) 155307.
[61] Ka-Di Zhu, Wai-Sang Li, Effect of quantum lattice fluctuations on quantum coherent oscillations in a coherently driven quantum dot-cavity system, Phys Lett A 314 (2003) 380.
[62] C.-H.Yuan, K. D. Zhu, and X. Z. Yuan, Exciton entanglement in coupled quantum dots in a microcavity, Phys. Rev. A 75 (2007) 062309.
[63] A. Joshi, B. Anderson, and M. Xiao, Violation of Bell's inequality for two coupled quantum dots confined in a cavity, Phys. Rev. B 75 (2007) 125304.
[64] J. M. Raimond, M. Brune, and S. Haroche, Manipulating quantum entanglement with atoms and photons in a cavity, Rev. Mod. Phys. 73 (2001) 565.
[65] Xiao-Zhong Yuan, Ka-Di Zhu, Wai-Sang Li, Influences of strong exciton-phonon interaction on two coupled quantum dots within cavity QED, Phys. Lett. A 329 (2004) 402.
[66] Fernando C. Lombardo, Paula I. Villar, Geometric phases in open systems: A model to study how they are corrected by decoherence, Phys Rev A 74 (2006) 042311.
[67] A. T. Rezakhani, P. Zanardi, Temperature effects on mixed-state geometric phase, Phys. Rev. A 73 (2006) 052117.
[68] X. Z.Yuan, H. S. Goan, K. D. Zhu, Non-Markovian reduced dynamics and entanglement evolution of two coupled spins in a quantum spin environment, Phys. Rev. B 75 (2007) 045331.
[69] M. Fujinaga, N. Hatano, The entanglement of the XY spin chain in a random magnetic field, Phys. Soc. Jpn. 76 (2007) 094001.
[70] M. Thorwart, P. Haggi, Decoherence and dissipation during a quantum xor gate operation, Phys. Rev. A 65 (2002) 012309.
[71] V. Turck, S. Rodt, et al., Effect of random field fluctuations on excitonic transitions of individual CdSe quantum dots, Phys. Rev. B 61 (2001) 9944.
[72] R. Heitz, I. Mukhametzhanov, et al., Enhanced Polar Exciton-LO-Phonon Interaction in Quantum Dots, Phys. Rev. Lett. 83 (1999) 4654.
[73] H. Kamda, H. Gotoh, et al., Emission of a Single Conjugated Polymer Chain Isolated in Its Single Crystal Monomer Matrix, Phys. Rev. Lett. 87 (2002) 087401.
[1]J.I.Cirac and P.Zoller,Preparation of macroscopic superpositions in many-atom systems, Phys. Rev. A 50 (1994) R2799.
[2] Shi-Biao Zheng, One-Step Synthesis of Multiatom Greenberger-Horne-Zeilinger States, Phys. Rev. Lett. 87 (2001) 230404.
[3] Shi-Biao Zheng, Generation of entangled states of multiple trapped ions in thermal motion, Phys. Rev. A 70 (2004) 045804.
[4] I. E. Linington and N. V. Vitanov, Robust creation of arbitrary-sized Dicke states of trapped ions by global addressing, Phys. Rev. A 77 (2008) 010302.
[5] W. X. Yang, Z. M. Zhan, and J. H. Li, Efficient scheme for multipartite entanglement and quantum information processing with trapped ions, Phys. Rev. A 72 (2005) 062108.
[6] J. A. Jones, M.Mosca, and R. H. Hansen, Implementation of a quantum search algorithm on a quantum computer, Nature (London) 393 (1998) 344.
[7] J. Q. You, J. S. Tsai, and Franco Nori, Controllable manipulation and entanglement of macroscopic quantum states in coupled charge qubits, Phys. Rev. B 68 (2003) 024510.
[8] F. Plastina, R. Fazio, and G. M. Palma, Macroscopic entanglement in Josephson nanocircuits, Phys. Rev. B 64 (2001)113306.
[9] L. F. Wei,Y. X. Liu, and F. Nori, Generation and Control of Greenberger-Horne-Zeilinger Entanglement in Superconducting Circuits, Phys. Rev. Lett. 96(2006)246803.
[10] L. F. Wei,Yu-xi Liu, M. J. Storcz, and F. Noril, Macroscopic Einstein-Podolsky-Rosen pairs in superconducting circuits, Phys. Rev. A 73 (2006) 052307.
[11] D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, Bell's theorem without inequalities, Am. J. Phys. 58, (1990) 1131.
[12] W. Dur, G. Vidal, and J. I. Cirac, Three qubits can be entangled in two inequivalent ways, Phys. Rev. A 62 (2000) 062314.
[13] M. Eib, N. Kiese, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, Experimental Realization of a Three-Qubit Entangled W State, Phys. Rev. Lett. 92 (2004) 077901.
[14] C. F. Roos, M. Riebe, H. Haffner, W. Hansel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, Control and Measurement of Three-Qubit Entangled States, Science 304 (2004) 1478.
[15] H. Mikami, Y. Li, K. Fukuoka, and T. Kobayashi, New High-Efficiency Source of a Three-Photon W State and its Full Characterization Using Quantum State Tomography, Phys. Rev. Lett. 95 (2005)150404.
[16] H. Haffner, W. Hansel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Korber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Guhne, W. Dur, and R. Blatt, Scalable multiparticle entanglement of trapped ions, Nature (London) 438 (2005) 643.
[17] R. Raussendorf and Hans J. Briegel, A One-Way Quantum Computer, Phys. Rev. Lett. 86(2001)5188.
[18] Hans J. Briegel and R. Raussendorf, Persistent Entanglement in Arrays of Interacting Particles, Phys. Rev. Lett. 86 (2001) 910.
[19] W. Dur and H. J. Briegel, Stability of Macroscopic Entanglement under Decoherence, Phys. Rev. Lett. 92 (2004) 180403.
[20] M. Borhani and D. Loss, Cluster states from Heisenberg interactions, Phys. Rev. A 71 (2005)034308.
[21] Shi-Biao Zheng, Generation of cluster states in ion-trap systems, Phys. Rev. A 73 (2006)065802.
[22] X. B. Zou, K. Pahlke, and W. Mathis, Quantum entanglement of four distant atoms trapped in different optical cavities, Phys. Rev. A 69 (2004) 052314.
[23] X. B. Zou and W. Mathis, Generating a four-photon polarization-entangled cluster state, Phys. Rev. A 71 (2005) 032308.
[24] X. B. Zou and W. Mathis, Schemes for generating the cluster states in microwave cavity QED, Phys. Rev. A 72 (2005) 013809.
[25] C. L. Jiang, M. F. Fang and Y. H. Hu , Efficient scheme of quantum SWAP gate and multi-atom cluster state via cavity QED, Chinese Physics B, 17 (2008)190.
[26] P. Dong, Zheng-Yuan Xue, M. Yang, and Zhuo-Liang Cao, Generation of cluster states, Phys. Rev. A 73 (2006) 033818.
[27] E. M. Becerra-Casto, W. B. Cardoso, A. T. Avelar, and B. Baseia, Generation of four-qubit cluster of entangled coherent states in bimodal QED cavities, e-print arXiv:quant-ph/0709.001 Ov1.
[28] J. Q. You, X. B. Wang, T. Tanamoto, and F. Nori, Efficient one-step generation of large cluster states with solid-state circuits, Phys. Rev. A 75 (2007) 052319.
[29] Z. Y. Xue and Z. D. Wang, Simple unconventional geometric scenario of one-way quantum computation with superconducting qubits inside a cavity, Phys. Rev. A 75 (2007)064303.
[30] Gang Chen, Zidong Chen, Lixian Yu, and Jiuqing Liang, One-step generation of cluster states in superconducting charge qubits coupled with a nanomechanical resonator, Phys. Rev. A 76 (2007) 024301.
[31] P. Walther, K. J. Resch, T. Rudolph, E. Schenk, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, Experimental one-way quantum computing, Nature (London) 434 (2005) 169. :
[32] N. Kiesel, C. Schmid, U. Weber, G. Toth, O. Guhne, R. Ursin, and H. Weinfurter, Experimental Analysis of a Four-Qubit Photon Cluster State, Phys. Rev. Lett. 95, (2005)210502.
[33] G. Vallone, E. Pomarico, P. Mataloni, F. De Martini, and V. Berardi, Realization and Characterization of a Two-Photon Four-Qubit Linear Cluster State, Phys. Rev. Lett. 98(2007)180502.
[34] M. Barbieri, C. Cinelli, F. De Martini, and P. Mataloni, Polarization-momentum hyperentangled states: Realization and characterization, Phys. Rev. A 72 (2005) 052110.
[35] S. B. Zheng and G. C. Guo, Efficient Scheme for Two-Atom Entanglement and Quantum Information Processing in Cavity QED, Phys. Rev. Lett. 85 (2000) 2392.
[36] S. Osnaghi, et al., Coherent Control of an Atomic Collision in a Cavity, Phys. Rev. Lett. 87 (2002) 037902.
[37] B .Yu, W. Z. Zhou, G. C. Guo, et al., Robust high-fidelity teleportation of an atomic state through the detection of cavity decay, Phys. Rev. A, 70 (2004) 014302.
[38] M. X. Lin, et al., Scheme for implementing quantum dense coding via cavity QED, Phys. Lett. A, 313 (2003) 351.
[39] P. Bertet et al., A complementarity experiment with an interferometer at the quantum-classical boundary, Nature (London) 411 (2001) 166.
[40] J. McKeever, et al., Deterministic generation of single photons from one atom trapped in a cavity, Science 303 (2004) 1992.
[41] P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinlcse, and G. Rempe, Cavity cooling of a single atom, Nature 428 (2004) 50.
[42] G. R. Guthohrlein, A single ion as a nanoscopic probe of an optical field, Nature 414 (2001)49.
[43] E. Solano, G. S. Agarwal, and H. Walther, Strong-Driving-Assisted Multipartite Entanglement in Cavity QED, Phys. Rev. Lett. 90 (2003) 027903.
[44] S. B. Zheng, Quantum-information processing and multiatom-entanglement engineering with a thermal cavity, Phys. Rev. A 66 (2002) 060303(R).
[45] Liu Ye, Long-Bao Yu, and Guang-Can Guo, Generation of entangled states in cavity QED, Phys. Rev. A 72 (2005) 034304 (also seen the erratum: Phys. Rev. A 73 (2006) 029907(E)).
[46] M. Bina, F. Casagrande, A. Lulli, and E. Solano, Monitoring atom-atom entanglement and decoherence in a solvable tripartite open system in cavity QED, Phys. Rev. A 77 (2008) 033839.
[47] P. Lougovski,E. Solano, and H. Walther, Generation and purification of maximally entangled atomic states in optical cavities, Phys. Rev. A 71 (2005) 013811.
[48] Jun-Qi Li, Gang Chen, and J.-Q. Liang, One-step generation of cluster states in microwave cavity QED, Phys. Rev. A 77 (2008) 014304.
[49] C.-Y. Chen and M. Feng, Suppression of the heating effect in a geometric logic gating in a strong-driving-assisted cavity QED scheme, Physical Review A 77 (2008) 012325.
[50] Xun-Li Feng, Zisheng Wang, Chunfeng Wu, L. C. Kwek, C. H. Lai, and C. H. Oh, Scheme for unconventional geometric quantum computation in cavity QED, Physical Review A 75 (2007) 052312.
[51] Yong Li, Li Zheng, Yu-xi Liu, and C. P. Sun, Correlated photons and collective excitations of a cyclic atomic ensemble, Physical Review A 73 (2006) 043805.
[52] C.Y. Chen, M. Feng, X. L. Zhang, and K. L. Gao, Strong-driving-assisted unconventional geometric logic gate in cavity QED, Phys. Rev. A 73 (2006) 032344.
[53] C.Y.Chen, M. Feng, and K. L.Gao, Superposition and entanglement of mesoscopic squeezed vacuum states in cavity QED, Phys. Rev.A 73 (2006) 034305.