纠缠与量子相变关系及量子控制的理论研究
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摘要
量子信息学是量子理论与信息学交叉而产生的新兴学科,它的出现给未来的科技发展带来了美好的前景。量子信息学的发展与完善离不开对量子纠缠和量子控制等相关问题的深入研究。本文就量子纠缠与量子控制的一些问题进行了理论探讨,并得到了一些有意义的结果。
本文大体可分为四个部分。第一章和第二章构成本文的第一部分,第一章里较为系统的介绍了研究量子纠缠、量子控制的重要意义,以及目前的研究进展。第二章中我们介绍了与本文相关的量子信息学的基本知识。
本文的第二部分由第三章和第四章构成,主要讨论了量子多体系统中量子纠缠与量子相变的关系。在第三章中,我们对狄克模型进行了简单的介绍,并研究了在具有偶极相互作用的狄克模型中子系统的纠缠性质,以及量子相变现象。研究表明,子系统间的纠缠性质可以很好的反应量子相变的发生,原子间的偶极相互作用对子系统间的纠缠有重要影响。在第四章里,我们介绍了XY自旋链,通过研究与自旋链耦合的中心粒子间的纠缠性质,讨论了自旋链环境相变及温度对中心粒子间纠缠的影响。我们的研究表明,中心粒子间的纠缠性质和系统的初态有着密切的联系。在自旋链温度接近绝对零度时,中心粒子间的纠缠能够反应自旋链的相变现象,当自旋链温度升高时,自旋链自身的量子相变现象被热力学涨落淹没,温度还会引发中心粒子出现退纠缠现象。
第五章是本文的第三部分,在这一章里,我们研究了量子纠缠在量子信息里的一个重要应用——量子隐形传态,着重讨论了利用量子多体纠缠完成多量子比特的传送任务。通过一种矩阵符号,我们得到了一个描述量子隐形传态中量子通道和测量基之间关系的判据方程,并给出了方程的一些特解,这对寻找和利用多体系统纠缠资源实现多比特量子隐形传送具有一定的帮助。
本文的第四部分是第六章,我们介绍了量子控制的基本概念,回顾了前人的一个非相干量子控制方案,在前人的工作基础之上,提出了一个新的非相干控制方案,这个方案不仅可实现两能级系统控制,并且可以成功实现对有限维量子系统的控制。
文章的最后,给出了全文的总结和展望。
Quantum information theory,a combination of quantum mechanics and information theory,is a brand-new subject,whose appearance brings about a bright future for the development of science and technology.And the development and improvement of quantum information is dependent on the profound research on quantum entanglement and quantum control.This dissertation mainly discusses some problems related to quantum entanglement and quantum control in theory,and obtains some important results.
This dissertation consists of four parts.The first part includes Chapter 1 to Chapter 2.Chapter 1 introduces the significant meaning of quantum entanglement and quantum control systematically as well as their current studies.And the related theories to quantum information are presented in Chapter 2.
Part two is composed of Chapter 3 and Chapter 4,which chiefly discusses the relationships between quantum entanglement and quantum phase transition in multi-particle system. Chapter 3 begins with brief introduction of the Dicke model,and then demonstrates the research on the entanglement properties between subsystems as well as quantum phase transition in the Dicke model with the dipole-dipole interactions.The results demonstrate that the entanglement properties between subsystems can well signal the occurrence of quantum phase transition,and the dipole-dipole interactions have a great impact on the entanglement between the subsystems.The XY spin chain is presented in Chapter 4,and the entanglement evolution of bipartite spin-1/2 system coupled to a common surrounding XY chain in transverse fields at nonzero temperature is studied.The results indicate that the properties of entanglement between central particles are closed associated with the initial state of the system.When the temperature of the system is near absolute zero,the entanglement between central particles can reflect the quantum phase transition in spin chain.As the temperature increases,the quantum phase transition is washed out by thermodynamical fluctuations.In addition,the temperature can lead to disentanglement between central particles.
Chapter 5 alone consists of the third part,in which quantum teleportation,an important application of quantum entanglement in quantum information,is studied.And emphasis is placed on the study of multi-qubit teleportation by employing quantum multi-particle entanglement. By introducing matrix operator,the judgment equation reflecting the relationships between quantum channel and measurement basis in quantum teleportation is described and some special solutions of the equation is given,which can help to seek and use multi-particles entanglement recourses in order to realize the quantum teleportation.
Chapter 6 is the fourth part,which presents the concepts of quantum control,and reviews a previous incoherent quantum control scheme.Based on the former scheme,a new scheme is put forward,which can not only realize the controlling of two-level quantum system,but also can be extended to control the finite-dimensional quantum system.
Finally,the results are summarized and suggestions are given for future research work.
本文大体可分为四个部分。第一章和第二章构成本文的第一部分,第一章里较为系统的介绍了研究量子纠缠、量子控制的重要意义,以及目前的研究进展。第二章中我们介绍了与本文相关的量子信息学的基本知识。
本文的第二部分由第三章和第四章构成,主要讨论了量子多体系统中量子纠缠与量子相变的关系。在第三章中,我们对狄克模型进行了简单的介绍,并研究了在具有偶极相互作用的狄克模型中子系统的纠缠性质,以及量子相变现象。研究表明,子系统间的纠缠性质可以很好的反应量子相变的发生,原子间的偶极相互作用对子系统间的纠缠有重要影响。在第四章里,我们介绍了XY自旋链,通过研究与自旋链耦合的中心粒子间的纠缠性质,讨论了自旋链环境相变及温度对中心粒子间纠缠的影响。我们的研究表明,中心粒子间的纠缠性质和系统的初态有着密切的联系。在自旋链温度接近绝对零度时,中心粒子间的纠缠能够反应自旋链的相变现象,当自旋链温度升高时,自旋链自身的量子相变现象被热力学涨落淹没,温度还会引发中心粒子出现退纠缠现象。
第五章是本文的第三部分,在这一章里,我们研究了量子纠缠在量子信息里的一个重要应用——量子隐形传态,着重讨论了利用量子多体纠缠完成多量子比特的传送任务。通过一种矩阵符号,我们得到了一个描述量子隐形传态中量子通道和测量基之间关系的判据方程,并给出了方程的一些特解,这对寻找和利用多体系统纠缠资源实现多比特量子隐形传送具有一定的帮助。
本文的第四部分是第六章,我们介绍了量子控制的基本概念,回顾了前人的一个非相干量子控制方案,在前人的工作基础之上,提出了一个新的非相干控制方案,这个方案不仅可实现两能级系统控制,并且可以成功实现对有限维量子系统的控制。
文章的最后,给出了全文的总结和展望。
Quantum information theory,a combination of quantum mechanics and information theory,is a brand-new subject,whose appearance brings about a bright future for the development of science and technology.And the development and improvement of quantum information is dependent on the profound research on quantum entanglement and quantum control.This dissertation mainly discusses some problems related to quantum entanglement and quantum control in theory,and obtains some important results.
This dissertation consists of four parts.The first part includes Chapter 1 to Chapter 2.Chapter 1 introduces the significant meaning of quantum entanglement and quantum control systematically as well as their current studies.And the related theories to quantum information are presented in Chapter 2.
Part two is composed of Chapter 3 and Chapter 4,which chiefly discusses the relationships between quantum entanglement and quantum phase transition in multi-particle system. Chapter 3 begins with brief introduction of the Dicke model,and then demonstrates the research on the entanglement properties between subsystems as well as quantum phase transition in the Dicke model with the dipole-dipole interactions.The results demonstrate that the entanglement properties between subsystems can well signal the occurrence of quantum phase transition,and the dipole-dipole interactions have a great impact on the entanglement between the subsystems.The XY spin chain is presented in Chapter 4,and the entanglement evolution of bipartite spin-1/2 system coupled to a common surrounding XY chain in transverse fields at nonzero temperature is studied.The results indicate that the properties of entanglement between central particles are closed associated with the initial state of the system.When the temperature of the system is near absolute zero,the entanglement between central particles can reflect the quantum phase transition in spin chain.As the temperature increases,the quantum phase transition is washed out by thermodynamical fluctuations.In addition,the temperature can lead to disentanglement between central particles.
Chapter 5 alone consists of the third part,in which quantum teleportation,an important application of quantum entanglement in quantum information,is studied.And emphasis is placed on the study of multi-qubit teleportation by employing quantum multi-particle entanglement. By introducing matrix operator,the judgment equation reflecting the relationships between quantum channel and measurement basis in quantum teleportation is described and some special solutions of the equation is given,which can help to seek and use multi-particles entanglement recourses in order to realize the quantum teleportation.
Chapter 6 is the fourth part,which presents the concepts of quantum control,and reviews a previous incoherent quantum control scheme.Based on the former scheme,a new scheme is put forward,which can not only realize the controlling of two-level quantum system,but also can be extended to control the finite-dimensional quantum system.
Finally,the results are summarized and suggestions are given for future research work.
引文
[1]丛爽,量子力学系统控制导论,[M].科学出版社,2006.
[2]Einstein A,Podolsky B,Rosen N,Can quantum mechanical description of physical reality be considered complete?[J].Phys.Rev.1935,47:777-780.
[3]Schr(o|¨)dinger E,Probability relations between separated systems,Proc.Cambridge.[J].Philos.Soc.,1936,32:446-452.
[4]Bohm D,A suggested interpretation of the quantum theory in terms of 'hidden' variables,[J].Phys.Rev.1952,85:166-193.
[5]Bell J,On the Einstein-Podolsky-Rosen paradox,[J].Physics,1964,1:195-200.
[6]Nielson M A,Chuang I L,quantum computation and quantum information,[M].Cambridge University Press,2000.
[7]Feymann R P.Quantum theory,the church turing principle and the universal quantum computer.[J].International Journal of Theoretical Physics,1982,21:6-7.
[8]Bennett C H,Brassard G,Crepeau C,et al.Teleportating an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,[J].Phys.Rev.Lett,1993,70:1895.
[9]Shot P W,Algorithms for quantum computation:Discrete logarithms and factoring,1994 Proc.35th Annual symposium on the Foundations of Computer Science,124.
[10]Grover L K,Quantum Mechanics helps in searching for a needle in a haystack,[J].Phys.Rev.Lett.,1997,78:325.
[11]Plenio M B,Virmani S,An introduction to entanglement measures,[J].Quantum Inf Comput,2007,7:1-51.
[12]Ekert A K,Quantum cryptography based on Bell's theorem,[J].Phys.Rev.Let.,1991,67:661-663.
[13]Bennett C H and Wiesner S J,Communication via one- and two-particle operators on Einstein-Podolsky -Rosen states,[J].Phys.Rev.Lett.,1992,69:2881-2884.
[14]Raussendorf R and Briegel H J,A One-Way Quantum Computer,[J].Phys.Rev.Let.,2001,86:5188-5191.
[15]Raussendorf R,Browne D E,and Briegel H J,Measurement-based quantum computation on cluster states,[J].Phys.Rev.A.,2003,68:022312.
[16]Sachdev S,Quantum Phase Transition,[M].Cambridge University Press,Cambridge,1999.
[17]Dicke R H,Coherence in Spontaneous Radiation Processes,[J].Phys.Rev.,1954,93:99.
[18]Lipkin H J,Meshkov N,Glick A J,Validity of many-body approximation methods for a solvable model,[J].Nucl.Phys.,1965,62:188;1965,62:199;1965,62:211.
[19]Osborne T J,Nielsen M A,Entanglement in a simple quantum phase transition,[J].Phys.Rev.A,2002,66:032110.
[20]Osterloh A,Amico L,Falci G,Fazio R,Scaling of entanglement close to a quantum phase transition,[J].Nature(London),2002,416:608.
[21]Wootters W K,Entanglement of Formation of an Arbitrary State of Two Qubits,[J].Phys.Rev.Lett.,1998,80:2245.
[22]Vidal G,Latorre J I,Rico E,Kitaev A,Entanglement in Quantum Critical Phenomena,[J].Phys.Rev.Lett.,2003,90:227902.
[23]Wu L A,Sarandy M S,Lider D A,Quantum Phase Transitions and Bipartite Entanglement,[J].Phys.Rev.Lett.,2004,93:250404.
[24]Yang M F,Reexamination of entanglement and the quantum phase transition,[J].Phys.Rev.A,2005,71:030302.
[25]Chen Y,Zanardi P,Wang Z D,et al.Entanglement and Quantum Phase Transition in Low Dimensional Spin Systems[J].New Journal of Physics,2006,8:97;Chen Y,Wang Z D,Zhang F C,Exploring Quantum Phase Transitions with a Novel Sublattice Entanglement Scenario,[J].Phys.Rev.B,2006,73:224414.
[26]Gu S J,Deng S S,Li Y Q,Lin H Q,Entanglement and Quantum Phase Transition in the Extended Hubbard Model,[J].Phys.Rev.Lett.,2004,93:086402.
[27]Verstraete F,Popp M,Cirac J I,Entanglement versus Correlations in Spin Systems,[J].Phys.Rev.Lett.,2004,92:027901.
[28]Brukner C,Vedral V,Zeilinger A,Crucial role of quantum entanglement in bulk properties of solids,[J].Phys Rev.A,2006,73:012110;Cho S Y,Mckenzie R H,Quantum entanglement in the two-impurity Kondo model,[J].Phys.Rev.A,2006,73:012109.
[29]Chen Y,Wang Z D,Zhang F C,Exploring quantum phase transitions with a sublattice entanglement scenario,[J].Phys.Rev.B,2006,73:224414.
[30]Schlosshauer M,Decoherence,the measurement problem,and interpretations of quantum mechanics,[J].Rev.Mod.Phys.2004,76:1267.
[31]孙昌璞,衣学喜,周端陆,郁思夏,量子退相干问题,[M].曾谨言等编,量子力学新进展(第一辑),北京:北京大学出版社,2000;孙昌璞,张芃,量子绝热近似理论与Berry相因子:推广和应用,陈增兵,逯怀新,吴胜俊,张永德,量子纠缠与空间非定域性,[M].曾谨言等编,量子力学新进展(第二辑),北京大学出版社,2001.
[32]Huang G,Tarn T J,and Clark J W,On the controllability of quantum-mechanical systems,[J].J.Math.Phys.,1983,24:2608-2618.
[33]Ong C K,Huang G M,Tarn T,Clark J W,Invertibility of Quantum-Mechanical Control Systems,[J].Mathematical Systems Theory,1984,17:335-350.
[34]Clark J W,Ong C K,Tarn T J,et al.Quantum nondemolition filters.[M].Math.Systems Theory,1985,18:33-55.
[35]Lin E B,Quantum control theory,[J].Contemporary Mathematics,1989,97:269-278.
[36]D'Alessandro D,Dahleh M,Optimal Control of Two-level Quantum Systems,[J].IEEE Trans.Automat.Contr.,2001,46:866-876.
[37]Khaneja N,Brockett R,and Glaser S J,Time optimal control in spin systems,[J].Phys.Rev.A,2001,63:032308.
[38]Khaneja N,Glaser S J,and Brokett R,Sub-riemannian geometry and time optimal control of three spin systems:quantum gates and coherence transfer,[J].Phys.Rev.A,2002,65:032301.
[39]Ramakrishna V,Salapaka M V,Dahleh M,et al,Controllability of molecular systems,[J].Phys.Rev.A,1995,51:960- 966.
[40]Alessandro D D,Topological properties of reachable sets and the control of quantum bits,[J].Systems and Control Letters,2000,41:213-221.
[41]Lloyd S,Almost any quantum logic gate is universal,[J].Phys.Rev.Lett.,1995,75:346-349.
[42]Fu H,Schirmer S G,and Solomon A I,Complete controllability of finite-level quantum systems,[J].J.Phys.A:Math.Gen.,2001,34:1679-1690.
[43]Schirmer S G,Fu H,and Solomon A I,Complete controllability of quantum systems,[J].Phys.Rev.A,2000,63:063410.
[44]Altafini C,Controllability of quantum mechanical systems by root space decomposition of su(n),[J].J.Math.Phys.,2002,43:2051-2062.
[45]喀兴林.高等量子力学(第二版)[M].北京:高等教育出版社,2001.8.
[46]Peres A.Separability criterion for density matrices.[J].Phys.Rev.Lett.,1996,77(8):1413-1415.
[47]Vidal G,Werner R F.Computable measure of entanglement.[J].Phys.Rev.A,2002,65(3):032314(1-11).
[48]Bhom D.Quantum Theory.[M].Prentice Hall,Engiewood Cliffs,NJ 1951.
[49]Wootters W K and Zurek W H,A single quantum cannot be cloned,[J].Nature,1982,299:802-803.
[50]张永德.量子信息物理原理[M].北京:科学出版社,2005.
[51]Hepp K and Lieb E H,On the Superradiant Phase Transition for Molecules in a Quantized Radiation Field:The Dicke Maser Model,[J].Ann.Phys.(N.Y.) 1973,76:360-404.
[52]Y.K.Wang and F.T.Hioe,Phase Transition in the Dicke Model of Superradiance,[J].Phys.Kev.A,1973,7:831-836.
[53]Emary C and Brandes T,Quantum Chaos Triggered by Precursors of a Quantum Phase Transition:The Dicke Model,[J].Phys.Rev.Lett.2003,90:044101.
[54]C.Emary and T.Brandes,Chaos and the quantum phase transition in the Dicke model,[J].Phys.Rev.E 2003,67:066203.
[55]Chen G,Li J and Liang J Q,Critical property of the geometric phase in the Dicke model,[J].Phys.Rev.A,2006,74:054101.
[56]Plastina F,Liberti G and Carollo A,Scaling of Berry's phase close to the Dicke quantum phase transition,[J].Europhys.Lett.2006,76:182-188.
[57]Jarrett T C,Olaya-Castro A,and Johnson N F,Quantum optical properties of the radiation field in the Dicke model,[J].J.Phys.:Conf.Set.2007,84:012009;Optical signatures of quantum phase transitions in a light-matter system,[J].Europhys.Lett.2007,77:34001.
[58]Tolkunov D and Solenov D,Quantum phase transition in the multimode Dicke model,[J].Phys.Rev.B,2007,75:024402.
[59]Goto H and Ichimura K,Quantum phase transition in the generalized Dicke model:Inhomogeneous coupling and universality,[J].Phys.Rev.A,2008,77:053811.
[60]Emary C and Brandes T,Phase transitions in generalized spin-boson(Dicke) models,[J].Phys.Rev.A,2004,69:053804.
[61]Lee C F and Johnson N F,First-Order Superradiant Phase Transitions in a Multiqubit Cavity System,[J].Phys.Rev.Lett.2004,93:083001.
[62]Shindo D,Chavez A,Chumakov S M,and Klimov A B,Dynamical squeezing enhancement in the off-resonant Dicke model,[J].J.Opt.B:Quantum Semiclass.Opt.2004,6:34-40.
[63]Li Y,Wang Z D,and Sun C P,Quantum criticality in a generalized Dicke model,[J].Phys.Rev.A,2006,74:023815.
[64]Chen G,Zhao D and Chen Z,Quantum phase transition for the Dicke model with the dipole-dipole interactions,[J].J.Phys.B:At.Mol.Opt.Phys.2006,39:3315.
[65]Nemes M C,Furuya K,Pellegrino G Q,et al.Quantum entanglement and fixed point Hopf bifurcation,[J].Phys.Lett.A,2006,354:60.
[66]Alcalde M A,de Lemos A L L,and Svaiter N F,Functional methods in the generalized Dicke model,[J].J.Phys.A:Math.Theor.2007,40:11961.
[67]Friedberg R and Hartmann S R,Temporal evolution of superradiance in a small sphere,[J].Phys.Rev.A,1974,10:1728.
[68]Lawande S V,Jagatap B N and Puri R R,Laser phase and amplitude fluctuations in the fluorescent Dicke model of interacting atoms,[J].J.Phys.B:At.Mol.Phys.1985,18:1711.
[69]Chen G,Chen Z and Liang J Q,Self-organization of a Bose-Einstein condensate in an optical cavity,[J].Europhys.Lett.2007,80:40004.
[70]Scully M O and Zubairy M S,Quantum Optics[M].Cambridge University Press,Cambridge,1997;
[71]Hagley E,Maitre X,Nogues G,et al.Generation of Einstein-Podolsky-Rosen Pairs of Atoms,[J].Phys.Rev.Lett.1997,79:1.
[72]Rauschenbeutel A,Nogues G,Osnaghi S,et al.Step-by-Step Engineered Multiparticle Entanglement,[J].Science,2000,288:2024.
[73]Dutra S M,Knight P L and Moya-Cessa H,Large-scale fluctuations in the driven Jaynes-Cummings model,[J].Phys.Rev.A,1994,49:1993.
[74]Young D K,Zhang L,Awschalom D D and Hu E L,Coherent coupling dynamics in a quantum-dot microdisk laser,[J].Phys.Rev.B,2002,66:081307(R).
[75]Solomon G S,Pelton M and Yamamoto Y,Single-mode Spontaneous Emission from a Single Quantum Dot in a Three-Dimensional Microcavity,[J].Phys.Rev.Lett.2001,86:3903.
[76]Moller B,Artemyev M V,Woggon U and Wannemacher R,Coupled-resonator optical waveguides doped with nanocrystals,[J].Appl.Phys.Lett.2002,80:3253;Berglund A J,Doherty A C and Mabuchi H,Photon Statistics and Dynamics of Fluorescence Resonance Energy Transfer,[J].Phys.Rev.Lett.2002,89:068101.
[77]Johnson S G and Joannopoulos J D,Photonic Crystals:The Road from Theory to Practice[M].(Kluwer,New York) 2001;Hui P M and Johnson N F,in Solid State Physics[M].,edited by Ehrenreich H and Spaepen F,1995,49(Academic Press,New York).
[78]Kiraz A,Reese C,Gayral B,et al.,Cavity-quantum electrodynamics with quantum dots,[J].J.Opt.B,5(2003) 129.
[79]Yoshie T,Scherer A,Hendrickson J,et al.Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,[J].Nature,2004,432:200.
[80]Wallraff A,Schuster1 D I,Blaisl A,et al.Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,[J].Nature,2004,431:162.
[81]Guthohrlein G R,Keller M,Hayasaka K,et al.A single ion as a nanoscopic probe of an optical field,[J].Nature,2001,414:49.
[82]Imamoglu A,Awschalom D D,Burkard G,et al.Quantum Information Processing Using Quantum Dot Spins and Cavity QED,[J].Phys.Rev.Lett.1999,83:4204.
[83]Olaya-Castro A and Johnson N F,in Handbook of Theoretical and Computational Nanotechnology [M],edited by Rieth M.and Schommers W.(American Scientific Publishers,New York) 2004(Preprint:quantph/0406133).
[84]Michler P,Single Quantum Dots:Fundamentals,Applications and New Concepts[M].(Springer-Verlag,Berlin) 2003;Haug H and Koch S W,Quantum Theory of the Optical and Electronic Properties of Semiconductors[M].(World Scientific,Singapore) 2004;Johnson N F,Quantum dots:few-body,low-dimensional systems,[J].J.Phys.:Condens.Matter,1995,7:965.
[85]Sakoglu U,Tyo J S,Hyat M M,et al.Spectrally adaptive infrared photodetectors with bias-tunable quantum dots,[J].J.Opt.B,2004,21:7.
[86]Lambert N,Emary C and Brandes T,Entanglement and the Phase Transition in Single-Mode Superradiance,[J].Phys.Rev.Lett.2004,92:073602.
[87]Lambert N,Emary C,and Brandes T,Entanglement and entropy in a spin-boson quantum phase transition,[J].Phys.Rev.A,2005,71:053804.
[88]Reslen J,Quiroga L and Johnson N F,Direct equivalence between quantum phase transition phenomena in radiation-matter and magnetic systems:Scaling of entanglement,[J].Europhys.Lett.2005,69:8.
[89]Agarwal G S,Springer Tracts in Modern Physics[J].1974,70(Heidelberg:Springer).
[90]Makhlin Y,Schon G and Shnirman A,Josephson-junction qubits with controlled couplings,[J].Nature,1999,398:305.
[91]Makhlin Y,Schon G and Shnirman A,Quantum-state engineering with Josephson-junction devices,[J].Rev.Mod.Phys.2001,73:357.
[92]Quiroga L and Johnson N F,Entangled Bell and Greenberger-Horne-Zeilinger States of Excitons in Coupled Quantum Dots,[J].Phys.Rev.Lett.1999,83:2270.
[93]Jarrent T C,Lee C F,and Johnson N F,Optically controlled spin glasses in multiqubit cavity systems,[J].Phys.Rev.B.2006,74:121301(R).
[94]Lee C F,and Johnson N F,Spin-glasses in optical cavity,Europhys.Lett.2008,81:37004.
[95]Wang X and Mφmer K,Pairwise entanglement in symmetric multi-qubit systems,[J].Eur.Phys.J.D,2002,18:385.
[96]Holstein T and Primakoff H,Field Dependence of the Intrinsic Domain Magnetization of a Ferromagnet,[J].Phys.Rev.1949,58:1098.
[97]Klein A and Marshalek E R,Boson realizations of Lie algebras with applications to nuclear physics,[J].Rev.Mod.Phys.1991,63:375.
[98]Srednicki M,Entropy and area,[J].Phys.Rev.Lett.1993,71:666.
[99]Wehrl A,General properties of entropy,[J].Rev.Mod.Phys.1978,50:221.
[100]Meyer D A and Wallach N R,Global entanglement in multiparticle systems,[J].J.Math.Phys.2002,43,4273.
[101]L.Amico,R.Fazio,A.Osterloh,and V.Vedral,Entanglement in many-body systems,[J].Rev.Mod.Phys.2008,80,517.
[102]T.Senthil,Proceedings of the Conference on 'Recent Progress in Many-Body Theories,'[C].Santa Fe,New Mexico(USA),Aug 23-27,2004.
[103]Kitaev A Y,Fault-tolerant quantum computation by anyons,[J].Ann.Phys.2003,303:2;Moessnet R and Sondhi S L,Resonating Valence Bond Phase in the Triangular Lattice Quantum Dimer Model,[J].Phys.Rev.Lett.2001,86:1881;Levin M A and Wen X G,String-net condensation:A physical mechanism for topological phases,[J].Phys.Rev.B,2005,71:045110.
[104]Fendley P and Fradkin E,Realizing non-Abelian statistics in time-reversal-invariant systems,[J].Phys.Rev.B,2005,72:024412;
[105]Kitaev A and Preskill J,Topological Entanglement Entropy,[J].Phys.Rev.Lett.2006,96:110404;Levin M A and Wen X G,Detecting Topological Order in a Ground State Wave Function,[J].Phys.Rev.Lett.2006,96,110405.
[106]Brennen G K,An observable measure of entanglement for pure states of multi-qubit systems,[J].Quantum Inf.Comput.2003,3:619.
[107]de Oliveira T R,Rigolin G,and de Oliveira M C,[J].Phys.Rev.A,2006,73:010305(R);de Oliveira T R,Rigolin G,de Otiveira M C and Miranda E,Multipartite Entanglement Signature of Quantum Phase Transitions,[J].Phys.Rev.Lett.2006,97:170401.
[108]Yi X X,Cui H T,Wang L C,Entanglement induced in spin-1/2 particles by a spin chain near its critical points,Phys.Rev.A,2006,74:054102.
[109]Sun Z,Wang X G,Sun C P,Disentanglement in a quantum-critical environment,[J].Phys.Rev.A,2007,75:062312.
[110]Yuan Z G,Zhang P,Li S S,Disentanglement of two qubits coupled to an XY spin chain:Role of quantum phase transition,Phys.Rev.A,2007,76:04211&
[111]Ma X S,Wang A M,Cao Y,Entanglement evolution of three-qubit states in a quantum-critical environment,[J].Phys.Rev.B,2007,76:155327.
[112]Ai Q,Shi T,Long G,Sun C P,Induced Entanglement Enhanced by Quantum Criticality,[J].Phys.Rev.A,2008,78:022327.
[113]Cormick C and Paz J P,Decoherence of Bell states by local interactions with a dynamic spin environment,[J].Phys.Rev.A,2008,78:012357.
[114]Micheli A,Brennen G K,ZoUer P,A toolbox for lattice spin models with polar molecules,[J].Nature Phys.,2006,2:341;Brennen G K,Micheli A,Zoller P,Designing spin-1 lattice models using polar molecules[J].New J.Phys.,2007,9:138.
[115]Duan L -M,Demler E,Lukin M D,Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices,[J].Phys.Rev.Lett.2003,91:090402;Porras D,Cirac J I,Effective Quantum Spin Systems with Trapped Ions,[J].Phys.Rev.Lett.2004,92:207901.
[116]Porras D,Cirac J I,Effective Quantum Spin Systems with Trapped Ions,[J].Phys.Rev.Lett.2004,92:207901;Deng X L,Porras D,Cirac J I,Quantum phases of interacting phonons in ion traps,e-print quant-ph/0509197.
[117]Hartmann M J,Brandao F G S L,and Plenio M B,Effective Spin Systems in Coupled Microcavities,[J].Phys.Rev.Lett.2007,99:160501.
[118]Pachos J K,Plenio M B,Three-Spin Interactions in Optical Lattices and Criticality in Cluster Hamiltonians,[J].Phys.Rev.Lett.2004,93:056402.
[119]Bose S,Quantum Communication through an Unmodulated Spin Chain,[J].Phys.Rev.Lett.2003,91:207901.
[120]Bayat A,Karimipour V,Thermal effects on quantum communication through spin chains,[J].Phys.Rev.A,2005,71:042330.
[121]Osborne T J,Linden N,Propagation of quantum information through a spin system,[J].Phys.Rev.A,2004,69:052315.
[122]Karbach P,Stolze J,Spin chains as perfect quantum state mirrors,[J].Phys.Rev.A,2005,72:030301(R).
[123]Romito A and Rosario Fazio,Solid-state quantum communication with Josephson arrays,[J].Phys.Rev.B,2005,71:100501(R).
[124]Anderson P W,Random-Phase Approximation in the Theory of Superconductivity,[J].Phys.Rev.1958,112:1900.
[125]Barouch E and McCoy B M,Statistical Mechanics of the XY Model.Ⅰ,[J].Phys.Rev.A,1970,2:1075;Statistical Mechanics of the XY Model.Ⅱ.Spin-Correlation Functions,[J].Phys.Rev.A,1971,3:786.
[126]Carollo A,Pachos J K,Geometric Phases and Criticality in Spin-Chain Systems,[J].Phys.Rev.Lett.2005,95:157203.
[127]Zhu S L,Scaling of Geometric Phases Close to the Quantum Phase Transition in the XY Spin Chain,[J].Phys.Rev.Lett.2006,96:077206.
[128]Zanardi P,Paunkovi(?) N,Ground state overlap and quantum phase transitions,[J].Phys.Rev.E,2006,74:031123;Zanardi P,Quan H T,Wang X,Sun C P,Mixed-state fidelity and quantum criticality at finite temperature,[J].Phys.Rev.A,2007,75:032109;Cozzini M,Giorda P,Zanardi P,Quantum phase transitions and quantum fidelity in free fermion graphs,[J].Phys.Rev.B,2007,75:014439.
[129]Zanardi P,Giorda P,Cozzini M,Information-Theoretic Differential Geometry of Quantum Phase Transitions,[J].Phys.Rev.Lett.,2007,99:100603.
[130]Lieb E,Schultz T,Mattis D,Two soluble models of an antiferromagnetic chain,[J].Ann.Phys.(N.Y.),1961,16:407-466.
[131]Uhlmann A,The "transition probability" in the state space of a*-algebra[J].Rep.Math.Phys.,1976,9:273;
[132]Quan H T,Song Z,Liu X F,Zanardi P,Sun C P,Decay of Loschmidt Echo Enhanced by Quantum Criticality,[J].Phys.Rev.Lett.2006,96:140604.
[133]Rossini D,Calarco T,Giovaunetti V,Montangero S,Fazio R,Decoherence induced by interacting quantum spin baths,[J].Phys.Rev.A,2007,75:032333.
[134]Wang L C,Cui H T,Yi X X,Decoherence induced by spin chain environment,[J].Chin.Phys.Lett.,2006,23:2648.
[135]Wang L C,Huang X L,Yi X X,Decoherence induced in spin-1/2 particles by spin chain environment at finite temperature[J].Phys.Lett.A,2007,368:362-365.
[136]Ou Y C,Fan H,Decoherence of a central quantum system coupled to an XY spin chain,[J].J.PHYS.A,2006,40(10):2455-2461.
[137]Yi X X,Wang W,Geometric phases induced in auxiliary qubits by many-body systems near their critical points,[J].Phys.Rev.A,2007,75:032103.
[138]Wang L C,Huang X L,Yi X X,Landau-Zener transition of a two-level system driven by a spin chain near its critical points,[J].Euro.Phys.J.D,2008,46:345-349.
[139]Yuan Z G,Zhang P,Li S S,Loschmidt echo and Berry phase of a quantum system coupled to an XY spin chain:Proximity to a quantum phase transition,[J].Phys.Rev.A,2007,75:012102.
[140]S.Katsura,Statistical Mechanics of the Anisotropic Linear Heisenberg Model,[J].Phys.Rev.1962,127:1508.
[141]Bouwmeester D,Pan J W,Mattle K,Eibl M,Weinfrurter H,Zeilinger A,Expreimental quantum teleportion,[J].Nature,1997,390:575-579.
[142]Boschi D,Branca S,De Martini F et al,Experimental realization of teleportation an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,[J].Phys Rev.Lett.,1998,80(6):1121-1125
[143]Vaidman L.Teleportation of quantum states.[J].Phys.Rev.A,1994,49(2):1473-1476
[144]Furusawa M A,Sorensen J L,Braunstein S Let al.Unconditional quantum teleportation,[J].Science,1998,282(5389):706-709.
[145]Nielsen M A,Knill E,Laflamme R.Complete quantum teleportation using nuclear maenetic resonance.[J].Nature.1998.396(6706):52-55.
[146]Lombardi E,Sciarrino F,Popescu Set al.Teleportation of a vacuum-one-photon qubit.[J].Phys.Rev.Lett,2002,88(7):070402-4
[147]Kim Y H,Kulik S P,Shih Y,Quantum teleportation of a polarization state with a complete Belt state measurement,[J].Phys.Rev.Lett.2001,86(7):1370-1373.
[148]de Riedmatten H,Marcikic 1,Tittel Wet al,Long distance quantum teleportation in a quantum relay configuration,[J].Phys.Rev.Lett,2004,92(4):047904-4.
[149]Zhao Z,Chen Y A,Zhang A N,et al,Experimental demonstration of five-photon entangledment and open-destination teleportation,[J].Nature,2004,430:54-58.
[150]Pan J W,Gasparoni S,Aspelmeyer M,et al,Experimental realization of freely propagating teleported qubit,[J].Nature,2003,421(6924):721-725
[151]Li W L,Li C F and Ouo G C,Probabilistic teleportation and entanglement matching,[J].Phys.Rev.A.2000,61:034301.
[152]Lu H and Guo G C.Teleportation of a two-particle entangled state via entaglement swapping.[J].Phys.Lett.A,2000,276(5-6):209-212.
[153]Shi B S,Jiang Y K and Guo G C,Probabilistic teleportation of two-particle entangled state,[J].Phy.Lett.A,2000,268:161-164.
[154]Gu Y J,Zheng Y Z and Guo G C,Probabilistic teleportation of an Arbitrary Two-particle State,[J].Chin.Phys.Lett.2001,18:1543-1545.
[155]Gao T,Wang Z X and Yan F L.Quantum Logic Network for Probabilistie Teleportation of Two-Particle State in a General Form,[J].Chin.Phys.Lett.2003,20:2094-2097.
[156]Cao M and Zhu S Q,Probabilistic Teleportation of n-Particle State via n Pairs of Entangled Particles,[J].Commum Theor.Phys.2005,43:69-72.
[157]Xia Y J,Fang J X,Zhu S Q,et al,Probabilistic Teleportation of an Arbitrary n-Particle Entangled State,[J].Commun.Theor.Phys.2005,44(1):51-54.
[158]Agrawal P and Pati A K,Prohabilistic quantum teleportation,[J].Phys.Lett.A,2002,305(1-2):12-17.
[159]Hsu L Y,Optimal information extraction in probabilistic teleportation,Phys.Rev.A,2002,66:012308.
[160]Pati A K and Agrawal,Probabilistic Teteportation of a Qudit.[J].Phys.Lett.A,2007,371(3):185-189.
[161]Pati A K and Agrawal P,Probabilistic teleportation and quantum operation,[J].J.Opt.B:quant.Semi.Opt.2004,6:844-848.
[162]Gordon G and Rigolin G,Generalized teleportation protocol,[J].Phys.Rev.A,2006,73:042309.
[163]Lee J,Min H and Oh S D,Multipartite entanglement for entanglement teleportation,[J].Phys.Rev.A,2002,66:052318.
[164]Rigolin G,Quantum teleportation of an arbitrary two-qubit state and its relation to multipartite entanglement,[J].Phys.Rev.A,2005,71:032303.
[165]Yeo Y,Chua W K,Teleportation and Dense Coding with Genuine Multipartite Entanglement,[J].Phys.Rev.Lett,2006,96.060502.
[166]Chert P X,Zhu S Y,Guo G C,General form of genuine multipartite entanglement quantum channels for teleportation,[J].Phys.Rev.A,2006,74:032324.
[167]Hughston L P,Ozsa R J,Wootters W K,A complete classification of quantum ensembles having a given density matrix,[J].Phys.Lett.A,1993,183:14.
[168]Li C,Song H S,Luo Y X,Criterion for general quantum teleportation,[J].Phys.Lett.A,2002,297:121.
[169]Li C,Song H S,and Zhou L,Alternative new notation for quantum information theory,arXiv:quant-ph/0303098.
[170]Romano R,D'Alessandro D,Incoherent control and entanglement for,two-dimensional coupled systems[J].Phys.Rev.A,2006,73:022323.
[171]Romano R,D'Alessandro D,Environment-Mediated Control of a Quantum System,[J].Phys.Rev.Left,2006,97:080402.
[172]Albertini F and D'Alessandro D,Notions of controllability for bilinear multilevel quantum system,IEEE transactions on automatic control,2003,48(8):1399-1403.
[173]陈宗海,董道毅,张陈斌,量子控制导论[M].,中国科学技术大学出版社,2005.
[174]V.Jurdjevic,Geometric Control Theory[M].,Cambridge:Cambridge University Press,1997.
[2]Einstein A,Podolsky B,Rosen N,Can quantum mechanical description of physical reality be considered complete?[J].Phys.Rev.1935,47:777-780.
[3]Schr(o|¨)dinger E,Probability relations between separated systems,Proc.Cambridge.[J].Philos.Soc.,1936,32:446-452.
[4]Bohm D,A suggested interpretation of the quantum theory in terms of 'hidden' variables,[J].Phys.Rev.1952,85:166-193.
[5]Bell J,On the Einstein-Podolsky-Rosen paradox,[J].Physics,1964,1:195-200.
[6]Nielson M A,Chuang I L,quantum computation and quantum information,[M].Cambridge University Press,2000.
[7]Feymann R P.Quantum theory,the church turing principle and the universal quantum computer.[J].International Journal of Theoretical Physics,1982,21:6-7.
[8]Bennett C H,Brassard G,Crepeau C,et al.Teleportating an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,[J].Phys.Rev.Lett,1993,70:1895.
[9]Shot P W,Algorithms for quantum computation:Discrete logarithms and factoring,1994 Proc.35th Annual symposium on the Foundations of Computer Science,124.
[10]Grover L K,Quantum Mechanics helps in searching for a needle in a haystack,[J].Phys.Rev.Lett.,1997,78:325.
[11]Plenio M B,Virmani S,An introduction to entanglement measures,[J].Quantum Inf Comput,2007,7:1-51.
[12]Ekert A K,Quantum cryptography based on Bell's theorem,[J].Phys.Rev.Let.,1991,67:661-663.
[13]Bennett C H and Wiesner S J,Communication via one- and two-particle operators on Einstein-Podolsky -Rosen states,[J].Phys.Rev.Lett.,1992,69:2881-2884.
[14]Raussendorf R and Briegel H J,A One-Way Quantum Computer,[J].Phys.Rev.Let.,2001,86:5188-5191.
[15]Raussendorf R,Browne D E,and Briegel H J,Measurement-based quantum computation on cluster states,[J].Phys.Rev.A.,2003,68:022312.
[16]Sachdev S,Quantum Phase Transition,[M].Cambridge University Press,Cambridge,1999.
[17]Dicke R H,Coherence in Spontaneous Radiation Processes,[J].Phys.Rev.,1954,93:99.
[18]Lipkin H J,Meshkov N,Glick A J,Validity of many-body approximation methods for a solvable model,[J].Nucl.Phys.,1965,62:188;1965,62:199;1965,62:211.
[19]Osborne T J,Nielsen M A,Entanglement in a simple quantum phase transition,[J].Phys.Rev.A,2002,66:032110.
[20]Osterloh A,Amico L,Falci G,Fazio R,Scaling of entanglement close to a quantum phase transition,[J].Nature(London),2002,416:608.
[21]Wootters W K,Entanglement of Formation of an Arbitrary State of Two Qubits,[J].Phys.Rev.Lett.,1998,80:2245.
[22]Vidal G,Latorre J I,Rico E,Kitaev A,Entanglement in Quantum Critical Phenomena,[J].Phys.Rev.Lett.,2003,90:227902.
[23]Wu L A,Sarandy M S,Lider D A,Quantum Phase Transitions and Bipartite Entanglement,[J].Phys.Rev.Lett.,2004,93:250404.
[24]Yang M F,Reexamination of entanglement and the quantum phase transition,[J].Phys.Rev.A,2005,71:030302.
[25]Chen Y,Zanardi P,Wang Z D,et al.Entanglement and Quantum Phase Transition in Low Dimensional Spin Systems[J].New Journal of Physics,2006,8:97;Chen Y,Wang Z D,Zhang F C,Exploring Quantum Phase Transitions with a Novel Sublattice Entanglement Scenario,[J].Phys.Rev.B,2006,73:224414.
[26]Gu S J,Deng S S,Li Y Q,Lin H Q,Entanglement and Quantum Phase Transition in the Extended Hubbard Model,[J].Phys.Rev.Lett.,2004,93:086402.
[27]Verstraete F,Popp M,Cirac J I,Entanglement versus Correlations in Spin Systems,[J].Phys.Rev.Lett.,2004,92:027901.
[28]Brukner C,Vedral V,Zeilinger A,Crucial role of quantum entanglement in bulk properties of solids,[J].Phys Rev.A,2006,73:012110;Cho S Y,Mckenzie R H,Quantum entanglement in the two-impurity Kondo model,[J].Phys.Rev.A,2006,73:012109.
[29]Chen Y,Wang Z D,Zhang F C,Exploring quantum phase transitions with a sublattice entanglement scenario,[J].Phys.Rev.B,2006,73:224414.
[30]Schlosshauer M,Decoherence,the measurement problem,and interpretations of quantum mechanics,[J].Rev.Mod.Phys.2004,76:1267.
[31]孙昌璞,衣学喜,周端陆,郁思夏,量子退相干问题,[M].曾谨言等编,量子力学新进展(第一辑),北京:北京大学出版社,2000;孙昌璞,张芃,量子绝热近似理论与Berry相因子:推广和应用,陈增兵,逯怀新,吴胜俊,张永德,量子纠缠与空间非定域性,[M].曾谨言等编,量子力学新进展(第二辑),北京大学出版社,2001.
[32]Huang G,Tarn T J,and Clark J W,On the controllability of quantum-mechanical systems,[J].J.Math.Phys.,1983,24:2608-2618.
[33]Ong C K,Huang G M,Tarn T,Clark J W,Invertibility of Quantum-Mechanical Control Systems,[J].Mathematical Systems Theory,1984,17:335-350.
[34]Clark J W,Ong C K,Tarn T J,et al.Quantum nondemolition filters.[M].Math.Systems Theory,1985,18:33-55.
[35]Lin E B,Quantum control theory,[J].Contemporary Mathematics,1989,97:269-278.
[36]D'Alessandro D,Dahleh M,Optimal Control of Two-level Quantum Systems,[J].IEEE Trans.Automat.Contr.,2001,46:866-876.
[37]Khaneja N,Brockett R,and Glaser S J,Time optimal control in spin systems,[J].Phys.Rev.A,2001,63:032308.
[38]Khaneja N,Glaser S J,and Brokett R,Sub-riemannian geometry and time optimal control of three spin systems:quantum gates and coherence transfer,[J].Phys.Rev.A,2002,65:032301.
[39]Ramakrishna V,Salapaka M V,Dahleh M,et al,Controllability of molecular systems,[J].Phys.Rev.A,1995,51:960- 966.
[40]Alessandro D D,Topological properties of reachable sets and the control of quantum bits,[J].Systems and Control Letters,2000,41:213-221.
[41]Lloyd S,Almost any quantum logic gate is universal,[J].Phys.Rev.Lett.,1995,75:346-349.
[42]Fu H,Schirmer S G,and Solomon A I,Complete controllability of finite-level quantum systems,[J].J.Phys.A:Math.Gen.,2001,34:1679-1690.
[43]Schirmer S G,Fu H,and Solomon A I,Complete controllability of quantum systems,[J].Phys.Rev.A,2000,63:063410.
[44]Altafini C,Controllability of quantum mechanical systems by root space decomposition of su(n),[J].J.Math.Phys.,2002,43:2051-2062.
[45]喀兴林.高等量子力学(第二版)[M].北京:高等教育出版社,2001.8.
[46]Peres A.Separability criterion for density matrices.[J].Phys.Rev.Lett.,1996,77(8):1413-1415.
[47]Vidal G,Werner R F.Computable measure of entanglement.[J].Phys.Rev.A,2002,65(3):032314(1-11).
[48]Bhom D.Quantum Theory.[M].Prentice Hall,Engiewood Cliffs,NJ 1951.
[49]Wootters W K and Zurek W H,A single quantum cannot be cloned,[J].Nature,1982,299:802-803.
[50]张永德.量子信息物理原理[M].北京:科学出版社,2005.
[51]Hepp K and Lieb E H,On the Superradiant Phase Transition for Molecules in a Quantized Radiation Field:The Dicke Maser Model,[J].Ann.Phys.(N.Y.) 1973,76:360-404.
[52]Y.K.Wang and F.T.Hioe,Phase Transition in the Dicke Model of Superradiance,[J].Phys.Kev.A,1973,7:831-836.
[53]Emary C and Brandes T,Quantum Chaos Triggered by Precursors of a Quantum Phase Transition:The Dicke Model,[J].Phys.Rev.Lett.2003,90:044101.
[54]C.Emary and T.Brandes,Chaos and the quantum phase transition in the Dicke model,[J].Phys.Rev.E 2003,67:066203.
[55]Chen G,Li J and Liang J Q,Critical property of the geometric phase in the Dicke model,[J].Phys.Rev.A,2006,74:054101.
[56]Plastina F,Liberti G and Carollo A,Scaling of Berry's phase close to the Dicke quantum phase transition,[J].Europhys.Lett.2006,76:182-188.
[57]Jarrett T C,Olaya-Castro A,and Johnson N F,Quantum optical properties of the radiation field in the Dicke model,[J].J.Phys.:Conf.Set.2007,84:012009;Optical signatures of quantum phase transitions in a light-matter system,[J].Europhys.Lett.2007,77:34001.
[58]Tolkunov D and Solenov D,Quantum phase transition in the multimode Dicke model,[J].Phys.Rev.B,2007,75:024402.
[59]Goto H and Ichimura K,Quantum phase transition in the generalized Dicke model:Inhomogeneous coupling and universality,[J].Phys.Rev.A,2008,77:053811.
[60]Emary C and Brandes T,Phase transitions in generalized spin-boson(Dicke) models,[J].Phys.Rev.A,2004,69:053804.
[61]Lee C F and Johnson N F,First-Order Superradiant Phase Transitions in a Multiqubit Cavity System,[J].Phys.Rev.Lett.2004,93:083001.
[62]Shindo D,Chavez A,Chumakov S M,and Klimov A B,Dynamical squeezing enhancement in the off-resonant Dicke model,[J].J.Opt.B:Quantum Semiclass.Opt.2004,6:34-40.
[63]Li Y,Wang Z D,and Sun C P,Quantum criticality in a generalized Dicke model,[J].Phys.Rev.A,2006,74:023815.
[64]Chen G,Zhao D and Chen Z,Quantum phase transition for the Dicke model with the dipole-dipole interactions,[J].J.Phys.B:At.Mol.Opt.Phys.2006,39:3315.
[65]Nemes M C,Furuya K,Pellegrino G Q,et al.Quantum entanglement and fixed point Hopf bifurcation,[J].Phys.Lett.A,2006,354:60.
[66]Alcalde M A,de Lemos A L L,and Svaiter N F,Functional methods in the generalized Dicke model,[J].J.Phys.A:Math.Theor.2007,40:11961.
[67]Friedberg R and Hartmann S R,Temporal evolution of superradiance in a small sphere,[J].Phys.Rev.A,1974,10:1728.
[68]Lawande S V,Jagatap B N and Puri R R,Laser phase and amplitude fluctuations in the fluorescent Dicke model of interacting atoms,[J].J.Phys.B:At.Mol.Phys.1985,18:1711.
[69]Chen G,Chen Z and Liang J Q,Self-organization of a Bose-Einstein condensate in an optical cavity,[J].Europhys.Lett.2007,80:40004.
[70]Scully M O and Zubairy M S,Quantum Optics[M].Cambridge University Press,Cambridge,1997;
[71]Hagley E,Maitre X,Nogues G,et al.Generation of Einstein-Podolsky-Rosen Pairs of Atoms,[J].Phys.Rev.Lett.1997,79:1.
[72]Rauschenbeutel A,Nogues G,Osnaghi S,et al.Step-by-Step Engineered Multiparticle Entanglement,[J].Science,2000,288:2024.
[73]Dutra S M,Knight P L and Moya-Cessa H,Large-scale fluctuations in the driven Jaynes-Cummings model,[J].Phys.Rev.A,1994,49:1993.
[74]Young D K,Zhang L,Awschalom D D and Hu E L,Coherent coupling dynamics in a quantum-dot microdisk laser,[J].Phys.Rev.B,2002,66:081307(R).
[75]Solomon G S,Pelton M and Yamamoto Y,Single-mode Spontaneous Emission from a Single Quantum Dot in a Three-Dimensional Microcavity,[J].Phys.Rev.Lett.2001,86:3903.
[76]Moller B,Artemyev M V,Woggon U and Wannemacher R,Coupled-resonator optical waveguides doped with nanocrystals,[J].Appl.Phys.Lett.2002,80:3253;Berglund A J,Doherty A C and Mabuchi H,Photon Statistics and Dynamics of Fluorescence Resonance Energy Transfer,[J].Phys.Rev.Lett.2002,89:068101.
[77]Johnson S G and Joannopoulos J D,Photonic Crystals:The Road from Theory to Practice[M].(Kluwer,New York) 2001;Hui P M and Johnson N F,in Solid State Physics[M].,edited by Ehrenreich H and Spaepen F,1995,49(Academic Press,New York).
[78]Kiraz A,Reese C,Gayral B,et al.,Cavity-quantum electrodynamics with quantum dots,[J].J.Opt.B,5(2003) 129.
[79]Yoshie T,Scherer A,Hendrickson J,et al.Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,[J].Nature,2004,432:200.
[80]Wallraff A,Schuster1 D I,Blaisl A,et al.Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,[J].Nature,2004,431:162.
[81]Guthohrlein G R,Keller M,Hayasaka K,et al.A single ion as a nanoscopic probe of an optical field,[J].Nature,2001,414:49.
[82]Imamoglu A,Awschalom D D,Burkard G,et al.Quantum Information Processing Using Quantum Dot Spins and Cavity QED,[J].Phys.Rev.Lett.1999,83:4204.
[83]Olaya-Castro A and Johnson N F,in Handbook of Theoretical and Computational Nanotechnology [M],edited by Rieth M.and Schommers W.(American Scientific Publishers,New York) 2004(Preprint:quantph/0406133).
[84]Michler P,Single Quantum Dots:Fundamentals,Applications and New Concepts[M].(Springer-Verlag,Berlin) 2003;Haug H and Koch S W,Quantum Theory of the Optical and Electronic Properties of Semiconductors[M].(World Scientific,Singapore) 2004;Johnson N F,Quantum dots:few-body,low-dimensional systems,[J].J.Phys.:Condens.Matter,1995,7:965.
[85]Sakoglu U,Tyo J S,Hyat M M,et al.Spectrally adaptive infrared photodetectors with bias-tunable quantum dots,[J].J.Opt.B,2004,21:7.
[86]Lambert N,Emary C and Brandes T,Entanglement and the Phase Transition in Single-Mode Superradiance,[J].Phys.Rev.Lett.2004,92:073602.
[87]Lambert N,Emary C,and Brandes T,Entanglement and entropy in a spin-boson quantum phase transition,[J].Phys.Rev.A,2005,71:053804.
[88]Reslen J,Quiroga L and Johnson N F,Direct equivalence between quantum phase transition phenomena in radiation-matter and magnetic systems:Scaling of entanglement,[J].Europhys.Lett.2005,69:8.
[89]Agarwal G S,Springer Tracts in Modern Physics[J].1974,70(Heidelberg:Springer).
[90]Makhlin Y,Schon G and Shnirman A,Josephson-junction qubits with controlled couplings,[J].Nature,1999,398:305.
[91]Makhlin Y,Schon G and Shnirman A,Quantum-state engineering with Josephson-junction devices,[J].Rev.Mod.Phys.2001,73:357.
[92]Quiroga L and Johnson N F,Entangled Bell and Greenberger-Horne-Zeilinger States of Excitons in Coupled Quantum Dots,[J].Phys.Rev.Lett.1999,83:2270.
[93]Jarrent T C,Lee C F,and Johnson N F,Optically controlled spin glasses in multiqubit cavity systems,[J].Phys.Rev.B.2006,74:121301(R).
[94]Lee C F,and Johnson N F,Spin-glasses in optical cavity,Europhys.Lett.2008,81:37004.
[95]Wang X and Mφmer K,Pairwise entanglement in symmetric multi-qubit systems,[J].Eur.Phys.J.D,2002,18:385.
[96]Holstein T and Primakoff H,Field Dependence of the Intrinsic Domain Magnetization of a Ferromagnet,[J].Phys.Rev.1949,58:1098.
[97]Klein A and Marshalek E R,Boson realizations of Lie algebras with applications to nuclear physics,[J].Rev.Mod.Phys.1991,63:375.
[98]Srednicki M,Entropy and area,[J].Phys.Rev.Lett.1993,71:666.
[99]Wehrl A,General properties of entropy,[J].Rev.Mod.Phys.1978,50:221.
[100]Meyer D A and Wallach N R,Global entanglement in multiparticle systems,[J].J.Math.Phys.2002,43,4273.
[101]L.Amico,R.Fazio,A.Osterloh,and V.Vedral,Entanglement in many-body systems,[J].Rev.Mod.Phys.2008,80,517.
[102]T.Senthil,Proceedings of the Conference on 'Recent Progress in Many-Body Theories,'[C].Santa Fe,New Mexico(USA),Aug 23-27,2004.
[103]Kitaev A Y,Fault-tolerant quantum computation by anyons,[J].Ann.Phys.2003,303:2;Moessnet R and Sondhi S L,Resonating Valence Bond Phase in the Triangular Lattice Quantum Dimer Model,[J].Phys.Rev.Lett.2001,86:1881;Levin M A and Wen X G,String-net condensation:A physical mechanism for topological phases,[J].Phys.Rev.B,2005,71:045110.
[104]Fendley P and Fradkin E,Realizing non-Abelian statistics in time-reversal-invariant systems,[J].Phys.Rev.B,2005,72:024412;
[105]Kitaev A and Preskill J,Topological Entanglement Entropy,[J].Phys.Rev.Lett.2006,96:110404;Levin M A and Wen X G,Detecting Topological Order in a Ground State Wave Function,[J].Phys.Rev.Lett.2006,96,110405.
[106]Brennen G K,An observable measure of entanglement for pure states of multi-qubit systems,[J].Quantum Inf.Comput.2003,3:619.
[107]de Oliveira T R,Rigolin G,and de Oliveira M C,[J].Phys.Rev.A,2006,73:010305(R);de Oliveira T R,Rigolin G,de Otiveira M C and Miranda E,Multipartite Entanglement Signature of Quantum Phase Transitions,[J].Phys.Rev.Lett.2006,97:170401.
[108]Yi X X,Cui H T,Wang L C,Entanglement induced in spin-1/2 particles by a spin chain near its critical points,Phys.Rev.A,2006,74:054102.
[109]Sun Z,Wang X G,Sun C P,Disentanglement in a quantum-critical environment,[J].Phys.Rev.A,2007,75:062312.
[110]Yuan Z G,Zhang P,Li S S,Disentanglement of two qubits coupled to an XY spin chain:Role of quantum phase transition,Phys.Rev.A,2007,76:04211&
[111]Ma X S,Wang A M,Cao Y,Entanglement evolution of three-qubit states in a quantum-critical environment,[J].Phys.Rev.B,2007,76:155327.
[112]Ai Q,Shi T,Long G,Sun C P,Induced Entanglement Enhanced by Quantum Criticality,[J].Phys.Rev.A,2008,78:022327.
[113]Cormick C and Paz J P,Decoherence of Bell states by local interactions with a dynamic spin environment,[J].Phys.Rev.A,2008,78:012357.
[114]Micheli A,Brennen G K,ZoUer P,A toolbox for lattice spin models with polar molecules,[J].Nature Phys.,2006,2:341;Brennen G K,Micheli A,Zoller P,Designing spin-1 lattice models using polar molecules[J].New J.Phys.,2007,9:138.
[115]Duan L -M,Demler E,Lukin M D,Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices,[J].Phys.Rev.Lett.2003,91:090402;Porras D,Cirac J I,Effective Quantum Spin Systems with Trapped Ions,[J].Phys.Rev.Lett.2004,92:207901.
[116]Porras D,Cirac J I,Effective Quantum Spin Systems with Trapped Ions,[J].Phys.Rev.Lett.2004,92:207901;Deng X L,Porras D,Cirac J I,Quantum phases of interacting phonons in ion traps,e-print quant-ph/0509197.
[117]Hartmann M J,Brandao F G S L,and Plenio M B,Effective Spin Systems in Coupled Microcavities,[J].Phys.Rev.Lett.2007,99:160501.
[118]Pachos J K,Plenio M B,Three-Spin Interactions in Optical Lattices and Criticality in Cluster Hamiltonians,[J].Phys.Rev.Lett.2004,93:056402.
[119]Bose S,Quantum Communication through an Unmodulated Spin Chain,[J].Phys.Rev.Lett.2003,91:207901.
[120]Bayat A,Karimipour V,Thermal effects on quantum communication through spin chains,[J].Phys.Rev.A,2005,71:042330.
[121]Osborne T J,Linden N,Propagation of quantum information through a spin system,[J].Phys.Rev.A,2004,69:052315.
[122]Karbach P,Stolze J,Spin chains as perfect quantum state mirrors,[J].Phys.Rev.A,2005,72:030301(R).
[123]Romito A and Rosario Fazio,Solid-state quantum communication with Josephson arrays,[J].Phys.Rev.B,2005,71:100501(R).
[124]Anderson P W,Random-Phase Approximation in the Theory of Superconductivity,[J].Phys.Rev.1958,112:1900.
[125]Barouch E and McCoy B M,Statistical Mechanics of the XY Model.Ⅰ,[J].Phys.Rev.A,1970,2:1075;Statistical Mechanics of the XY Model.Ⅱ.Spin-Correlation Functions,[J].Phys.Rev.A,1971,3:786.
[126]Carollo A,Pachos J K,Geometric Phases and Criticality in Spin-Chain Systems,[J].Phys.Rev.Lett.2005,95:157203.
[127]Zhu S L,Scaling of Geometric Phases Close to the Quantum Phase Transition in the XY Spin Chain,[J].Phys.Rev.Lett.2006,96:077206.
[128]Zanardi P,Paunkovi(?) N,Ground state overlap and quantum phase transitions,[J].Phys.Rev.E,2006,74:031123;Zanardi P,Quan H T,Wang X,Sun C P,Mixed-state fidelity and quantum criticality at finite temperature,[J].Phys.Rev.A,2007,75:032109;Cozzini M,Giorda P,Zanardi P,Quantum phase transitions and quantum fidelity in free fermion graphs,[J].Phys.Rev.B,2007,75:014439.
[129]Zanardi P,Giorda P,Cozzini M,Information-Theoretic Differential Geometry of Quantum Phase Transitions,[J].Phys.Rev.Lett.,2007,99:100603.
[130]Lieb E,Schultz T,Mattis D,Two soluble models of an antiferromagnetic chain,[J].Ann.Phys.(N.Y.),1961,16:407-466.
[131]Uhlmann A,The "transition probability" in the state space of a*-algebra[J].Rep.Math.Phys.,1976,9:273;
[132]Quan H T,Song Z,Liu X F,Zanardi P,Sun C P,Decay of Loschmidt Echo Enhanced by Quantum Criticality,[J].Phys.Rev.Lett.2006,96:140604.
[133]Rossini D,Calarco T,Giovaunetti V,Montangero S,Fazio R,Decoherence induced by interacting quantum spin baths,[J].Phys.Rev.A,2007,75:032333.
[134]Wang L C,Cui H T,Yi X X,Decoherence induced by spin chain environment,[J].Chin.Phys.Lett.,2006,23:2648.
[135]Wang L C,Huang X L,Yi X X,Decoherence induced in spin-1/2 particles by spin chain environment at finite temperature[J].Phys.Lett.A,2007,368:362-365.
[136]Ou Y C,Fan H,Decoherence of a central quantum system coupled to an XY spin chain,[J].J.PHYS.A,2006,40(10):2455-2461.
[137]Yi X X,Wang W,Geometric phases induced in auxiliary qubits by many-body systems near their critical points,[J].Phys.Rev.A,2007,75:032103.
[138]Wang L C,Huang X L,Yi X X,Landau-Zener transition of a two-level system driven by a spin chain near its critical points,[J].Euro.Phys.J.D,2008,46:345-349.
[139]Yuan Z G,Zhang P,Li S S,Loschmidt echo and Berry phase of a quantum system coupled to an XY spin chain:Proximity to a quantum phase transition,[J].Phys.Rev.A,2007,75:012102.
[140]S.Katsura,Statistical Mechanics of the Anisotropic Linear Heisenberg Model,[J].Phys.Rev.1962,127:1508.
[141]Bouwmeester D,Pan J W,Mattle K,Eibl M,Weinfrurter H,Zeilinger A,Expreimental quantum teleportion,[J].Nature,1997,390:575-579.
[142]Boschi D,Branca S,De Martini F et al,Experimental realization of teleportation an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,[J].Phys Rev.Lett.,1998,80(6):1121-1125
[143]Vaidman L.Teleportation of quantum states.[J].Phys.Rev.A,1994,49(2):1473-1476
[144]Furusawa M A,Sorensen J L,Braunstein S Let al.Unconditional quantum teleportation,[J].Science,1998,282(5389):706-709.
[145]Nielsen M A,Knill E,Laflamme R.Complete quantum teleportation using nuclear maenetic resonance.[J].Nature.1998.396(6706):52-55.
[146]Lombardi E,Sciarrino F,Popescu Set al.Teleportation of a vacuum-one-photon qubit.[J].Phys.Rev.Lett,2002,88(7):070402-4
[147]Kim Y H,Kulik S P,Shih Y,Quantum teleportation of a polarization state with a complete Belt state measurement,[J].Phys.Rev.Lett.2001,86(7):1370-1373.
[148]de Riedmatten H,Marcikic 1,Tittel Wet al,Long distance quantum teleportation in a quantum relay configuration,[J].Phys.Rev.Lett,2004,92(4):047904-4.
[149]Zhao Z,Chen Y A,Zhang A N,et al,Experimental demonstration of five-photon entangledment and open-destination teleportation,[J].Nature,2004,430:54-58.
[150]Pan J W,Gasparoni S,Aspelmeyer M,et al,Experimental realization of freely propagating teleported qubit,[J].Nature,2003,421(6924):721-725
[151]Li W L,Li C F and Ouo G C,Probabilistic teleportation and entanglement matching,[J].Phys.Rev.A.2000,61:034301.
[152]Lu H and Guo G C.Teleportation of a two-particle entangled state via entaglement swapping.[J].Phys.Lett.A,2000,276(5-6):209-212.
[153]Shi B S,Jiang Y K and Guo G C,Probabilistic teleportation of two-particle entangled state,[J].Phy.Lett.A,2000,268:161-164.
[154]Gu Y J,Zheng Y Z and Guo G C,Probabilistic teleportation of an Arbitrary Two-particle State,[J].Chin.Phys.Lett.2001,18:1543-1545.
[155]Gao T,Wang Z X and Yan F L.Quantum Logic Network for Probabilistie Teleportation of Two-Particle State in a General Form,[J].Chin.Phys.Lett.2003,20:2094-2097.
[156]Cao M and Zhu S Q,Probabilistic Teleportation of n-Particle State via n Pairs of Entangled Particles,[J].Commum Theor.Phys.2005,43:69-72.
[157]Xia Y J,Fang J X,Zhu S Q,et al,Probabilistic Teleportation of an Arbitrary n-Particle Entangled State,[J].Commun.Theor.Phys.2005,44(1):51-54.
[158]Agrawal P and Pati A K,Prohabilistic quantum teleportation,[J].Phys.Lett.A,2002,305(1-2):12-17.
[159]Hsu L Y,Optimal information extraction in probabilistic teleportation,Phys.Rev.A,2002,66:012308.
[160]Pati A K and Agrawal,Probabilistic Teteportation of a Qudit.[J].Phys.Lett.A,2007,371(3):185-189.
[161]Pati A K and Agrawal P,Probabilistic teleportation and quantum operation,[J].J.Opt.B:quant.Semi.Opt.2004,6:844-848.
[162]Gordon G and Rigolin G,Generalized teleportation protocol,[J].Phys.Rev.A,2006,73:042309.
[163]Lee J,Min H and Oh S D,Multipartite entanglement for entanglement teleportation,[J].Phys.Rev.A,2002,66:052318.
[164]Rigolin G,Quantum teleportation of an arbitrary two-qubit state and its relation to multipartite entanglement,[J].Phys.Rev.A,2005,71:032303.
[165]Yeo Y,Chua W K,Teleportation and Dense Coding with Genuine Multipartite Entanglement,[J].Phys.Rev.Lett,2006,96.060502.
[166]Chert P X,Zhu S Y,Guo G C,General form of genuine multipartite entanglement quantum channels for teleportation,[J].Phys.Rev.A,2006,74:032324.
[167]Hughston L P,Ozsa R J,Wootters W K,A complete classification of quantum ensembles having a given density matrix,[J].Phys.Lett.A,1993,183:14.
[168]Li C,Song H S,Luo Y X,Criterion for general quantum teleportation,[J].Phys.Lett.A,2002,297:121.
[169]Li C,Song H S,and Zhou L,Alternative new notation for quantum information theory,arXiv:quant-ph/0303098.
[170]Romano R,D'Alessandro D,Incoherent control and entanglement for,two-dimensional coupled systems[J].Phys.Rev.A,2006,73:022323.
[171]Romano R,D'Alessandro D,Environment-Mediated Control of a Quantum System,[J].Phys.Rev.Left,2006,97:080402.
[172]Albertini F and D'Alessandro D,Notions of controllability for bilinear multilevel quantum system,IEEE transactions on automatic control,2003,48(8):1399-1403.
[173]陈宗海,董道毅,张陈斌,量子控制导论[M].,中国科学技术大学出版社,2005.
[174]V.Jurdjevic,Geometric Control Theory[M].,Cambridge:Cambridge University Press,1997.