多种条件下原子体系量子纠缠的研究
|
摘要
量子纠缠态的制备和量子退相干机制的研究是量子信息学中两个重要的课题，是实现量子通信和量子计算机的基石。近几年的理论以及实验上的进展告诉我们，对于量子信息处理过程，比如量子离物传态、量子信息存储等等，纠缠态都是必不可少的资源，只有在可行的物理系统中实现便于集成、存储和操作的纠缠量子比特，量子信息才有意义。另一方面，如果考虑环境因素，我们所关心的系统与环境之间的相互作用将不可避免的导致退相干的发生，因此，研究退相干问题对量子信息技术无论从理论研究还是具体实现方面都是非常重要的。通常，在量子信息学中，环境被看作噪声，所以研究退相干的量子机制，研究量子噪声，是让量子信息论走向实用化的基础。
本文正是基于这样的原因，讨论了多种条件下原子体系的量子纠缠的问题。本文首先回顾量子信息学产生发展的概况，介绍量子信息学的基本理论，其中包括量子纠缠态的基本概念，对量子系统常用的量子主方程方法的导出过程和求解作了总结，这几方面的概述是本文所有工作的基础。第四章到第六章分别在几种条件下研究了原子体系量子纠缠的生成和应用。具体地，第四章研究了噪声对量子纠缠的影响，通常认为，量子噪声(环境)的影响总是负面的。我们从另一方面考虑，找出了量子噪声的积极意义——利用噪声来诱发纠缠，研究结果揭示出原子间的纠缠是原子衰变率的单值函数，对应于噪声强度的某一优化值能达到最大，系统与噪声的相互作用是产生纠缠的重要因素。第五章讨论了在凝聚体中产生的量子纠缠，对束缚在双势阱的二成份凝聚体系运用自旋-1／2近似的方法，最终生成对时间演化非单调的双模纠缠态。其中提供了一种研究多体问题的新方法——研究证明在半自旋近似下多体问题转化成了二体二能级的问题，大大简化了问题处理的难度。此外，还涉及到经典物理和量子物理的比较。第六章作为量子纠缠态在量子通信中的一个应用，提出一种新型的基于系统内在哈密顿量的基本量子逻辑门。我们首先引入了一种一般化的赝自旋算符，根据这种新的算符，研究普适的两比特相互作用哈密顿量，并且基于这样的哈密顿量用新的方法再现了一个基本的逻辑量子门，并证明这个新的量子门在功能上等价于Hadamard门和C-NOT门的联合操作。
总体来说，量子纠缠是量子信息学最基础、最核心的部分，是量子测量和退相干的潜在机制，对理解量子物理和经典物理的联系也至关重要。研究量子纠缠及其在量子信息学中的应用，不仅可以深刻理解量子力学的特性，而且又为信息传输和信息处理提供了实用的物理资源。本文所作的工作是关于量子纠缠理论方面的研究，对于这样一个发展迅速的研究领域，我们的工作仅仅涉及到很少的方面，对于纠缠态，更多更深层次的研究将等待我们去探索和发掘。
The preparation of quantum entangled states and quantum decoherence are two im-portant subjects in quantum information and are fundamental to quantum communicationand quantum computers. The development of quantum information both in theory and inexperiment indicates that quantum entangled states are indispensable resources in quan-tum information processes such as quantum teleportation, quantum information storage, etc.Therefore, quantum information demonstrates its significance only when entangled qubits,convenient for integration, storage and manipulation, are realized in experimentally-accessiblephysical systems. On the other hand, if the effects of the environment are taken into account,the interaction of the system in question and the environment will inevitably cause decoher-ence. Thus, the study of the process of the decoherence is very important for the theory andpractice of quantum information. Environment is often treated as noise in quantum informa-tion. Accordingly, study on the issue of the decoherence and quantum noise is fundamentalto applications of the quantum information theory.
The motivation of this dissertation arose from the above-stated important role of quan-tum entanglement in quantum information. In this dissertation, the question on quantumentanglement of atom-system under several different conditions is discussed. In the first threechapters, quantum information is briefly reviewed. Some basic quantum theories on quantumentanglement and master equation are discussed, including the definition, measurement andrealization of quantum entangled states and the derivation and solution of the master equa-tions. The above discussions consist of the background for this dissertation. From Chapter4 to Chapter 6, several possible schemes on the generation and application of atom-systementangled states are put forward and discussed under several different conditions. In detail,the influence of quantum noise on quantum entangled states is studied in Chapter 4. Gener-ally speaking, noise is negative for quantum information processes. However, noise-assistedentanglement preparation is investigated and it is found that noise may play a positive rolein entanglement generation. The dependence of the entanglement on the noise intensity aswell as on other parameters in the model is studied both analytically and numerically: theamount of entanglement behaves as monotonic function of the atom decay rate, and reachesits maximum value for an intermediate noise intensity. The results show that the interaction of system with noise is the important factor for entanglement generation. In Chapter 5, aspin-1/2 approximation method to study the quantum entanglement of two-component Bose-Einstein condensates trapped in double wells is proposed. The contours of entanglement withrespect to tunneling rate and time are found to be hyperbolic-like and non-monotonic. Inthis chapter, a new method to deal with multiple-body problem and to transform an ex-act many-body problem to a bipartite two-state problem under the spin-1/2 approximationis proposed. The new method greatly reduces the difficulty of the problem. In addition, thecomparison of classical and quantum physics is also discussed. As an application in quantumcommunication of quantum entangled states, a new fundamental quantum gate based on auniversal intrinsic interaction Hamiltonian is constructed in Chapter 6. New operators, thegeneralized pseudo-spin operators, are introduced and a universal intrinsic Hamiltonian witha two-qubit interaction is studied in terms of these operators. A fundamental quantum gateis constructed based on the universal Hamiltonian and it is shown that the role of the newquantum gate is functionally equivalent to the joint operation of Hadamard and C-Not gates.
In summary, the quantum entanglement, the core of the quantum information theory,is a potential mechanism for the quantum measurement and decoherence, and is criticallyimportant to the understanding of the boundary between quantum physics and classicalphysics. Therefore, the study of both quantum entanglement and its applications in quantuminformation are significant and necessary not only to the further understanding of the specialproperties of the quantum mechanics but also to the providing of practical physical resourcesfor information transmission and information processing. Some theoretical investigations onquantum entanglement are pursued in this dissertation. Quantum information theory is arapidly-developing research field. Further investigations of quantum entanglement will beundertaken in future.
本文正是基于这样的原因，讨论了多种条件下原子体系的量子纠缠的问题。本文首先回顾量子信息学产生发展的概况，介绍量子信息学的基本理论，其中包括量子纠缠态的基本概念，对量子系统常用的量子主方程方法的导出过程和求解作了总结，这几方面的概述是本文所有工作的基础。第四章到第六章分别在几种条件下研究了原子体系量子纠缠的生成和应用。具体地，第四章研究了噪声对量子纠缠的影响，通常认为，量子噪声(环境)的影响总是负面的。我们从另一方面考虑，找出了量子噪声的积极意义——利用噪声来诱发纠缠，研究结果揭示出原子间的纠缠是原子衰变率的单值函数，对应于噪声强度的某一优化值能达到最大，系统与噪声的相互作用是产生纠缠的重要因素。第五章讨论了在凝聚体中产生的量子纠缠，对束缚在双势阱的二成份凝聚体系运用自旋-1／2近似的方法，最终生成对时间演化非单调的双模纠缠态。其中提供了一种研究多体问题的新方法——研究证明在半自旋近似下多体问题转化成了二体二能级的问题，大大简化了问题处理的难度。此外，还涉及到经典物理和量子物理的比较。第六章作为量子纠缠态在量子通信中的一个应用，提出一种新型的基于系统内在哈密顿量的基本量子逻辑门。我们首先引入了一种一般化的赝自旋算符，根据这种新的算符，研究普适的两比特相互作用哈密顿量，并且基于这样的哈密顿量用新的方法再现了一个基本的逻辑量子门，并证明这个新的量子门在功能上等价于Hadamard门和C-NOT门的联合操作。
总体来说，量子纠缠是量子信息学最基础、最核心的部分，是量子测量和退相干的潜在机制，对理解量子物理和经典物理的联系也至关重要。研究量子纠缠及其在量子信息学中的应用，不仅可以深刻理解量子力学的特性，而且又为信息传输和信息处理提供了实用的物理资源。本文所作的工作是关于量子纠缠理论方面的研究，对于这样一个发展迅速的研究领域，我们的工作仅仅涉及到很少的方面，对于纠缠态，更多更深层次的研究将等待我们去探索和发掘。
The preparation of quantum entangled states and quantum decoherence are two im-portant subjects in quantum information and are fundamental to quantum communicationand quantum computers. The development of quantum information both in theory and inexperiment indicates that quantum entangled states are indispensable resources in quan-tum information processes such as quantum teleportation, quantum information storage, etc.Therefore, quantum information demonstrates its significance only when entangled qubits,convenient for integration, storage and manipulation, are realized in experimentally-accessiblephysical systems. On the other hand, if the effects of the environment are taken into account,the interaction of the system in question and the environment will inevitably cause decoher-ence. Thus, the study of the process of the decoherence is very important for the theory andpractice of quantum information. Environment is often treated as noise in quantum informa-tion. Accordingly, study on the issue of the decoherence and quantum noise is fundamentalto applications of the quantum information theory.
The motivation of this dissertation arose from the above-stated important role of quan-tum entanglement in quantum information. In this dissertation, the question on quantumentanglement of atom-system under several different conditions is discussed. In the first threechapters, quantum information is briefly reviewed. Some basic quantum theories on quantumentanglement and master equation are discussed, including the definition, measurement andrealization of quantum entangled states and the derivation and solution of the master equa-tions. The above discussions consist of the background for this dissertation. From Chapter4 to Chapter 6, several possible schemes on the generation and application of atom-systementangled states are put forward and discussed under several different conditions. In detail,the influence of quantum noise on quantum entangled states is studied in Chapter 4. Gener-ally speaking, noise is negative for quantum information processes. However, noise-assistedentanglement preparation is investigated and it is found that noise may play a positive rolein entanglement generation. The dependence of the entanglement on the noise intensity aswell as on other parameters in the model is studied both analytically and numerically: theamount of entanglement behaves as monotonic function of the atom decay rate, and reachesits maximum value for an intermediate noise intensity. The results show that the interaction of system with noise is the important factor for entanglement generation. In Chapter 5, aspin-1/2 approximation method to study the quantum entanglement of two-component Bose-Einstein condensates trapped in double wells is proposed. The contours of entanglement withrespect to tunneling rate and time are found to be hyperbolic-like and non-monotonic. Inthis chapter, a new method to deal with multiple-body problem and to transform an ex-act many-body problem to a bipartite two-state problem under the spin-1/2 approximationis proposed. The new method greatly reduces the difficulty of the problem. In addition, thecomparison of classical and quantum physics is also discussed. As an application in quantumcommunication of quantum entangled states, a new fundamental quantum gate based on auniversal intrinsic interaction Hamiltonian is constructed in Chapter 6. New operators, thegeneralized pseudo-spin operators, are introduced and a universal intrinsic Hamiltonian witha two-qubit interaction is studied in terms of these operators. A fundamental quantum gateis constructed based on the universal Hamiltonian and it is shown that the role of the newquantum gate is functionally equivalent to the joint operation of Hadamard and C-Not gates.
In summary, the quantum entanglement, the core of the quantum information theory,is a potential mechanism for the quantum measurement and decoherence, and is criticallyimportant to the understanding of the boundary between quantum physics and classicalphysics. Therefore, the study of both quantum entanglement and its applications in quantuminformation are significant and necessary not only to the further understanding of the specialproperties of the quantum mechanics but also to the providing of practical physical resourcesfor information transmission and information processing. Some theoretical investigations onquantum entanglement are pursued in this dissertation. Quantum information theory is arapidly-developing research field. Further investigations of quantum entanglement will beundertaken in future.
引文
[1] 郭光灿．量子信息引论．见：曾谨言，裴寿镛编．量子力学新进展(第一辑)．北京：北京大学出版社，2000：249-285．
[2] 李崇．量子通讯理论的矩阵表述：(博士学位论文)．大连：大连理工大学，2003．
[3] Einstein A, Podolsky B, Rosen N. Can Quantum-Mechanical Description of Physical Reality Be Considerd Complete? Phys. Rev., 1935, 47(10): 777-780.
[4] 宋鹤山．量子力学．大连：大连理工大学出版社，2004．
[5] Bennett C H, Brassard G. Quantum cryptography: public key distribution and coin tossing. Proc. IEEE Int. Conf. On Computers, Systems and Signal Processing, Bangalore, India (IEEE, New York), 1984, p175-179.
[6] Bennett C H. Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett., 1992, 68(21): 3121-3124.
[7] Hiskett P A, Rosenberg D, Peterson C G et al. Long-distance quantum key distribution in optical fibre. New Journal of Physics, 2006, 8: 193-196.
[8] Bennett C H, Brassard G, Crepeau C et al. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett., 1993, 70(13): 1895-1899.
[9] Bouwmeester D, Pan J W, Matle K et al. Experimental quantum teleportation. Nature, 1997, 390: 575-579.
[10] 张永德．综述：漫谈量子信息学．北京：人民日报，2003．
[11] Shor P W, Polynomial-Time algorithms for prime factorization and discrete logarithms on a quantum computer, Proceedings of the 35th Annual Symposium on Foundations of computer Science, Santa Fe NM: IEEE Computer Society Press, 1994, 20: 124-134.
[12] Grover L K. Quantum Mechanics Helps in searching for a Needle in a Haystack, Phys. Rev. Lett., 1997, 79(2): 325-328.
[13] Chuang I L, Vandersypen L M K, Zhou X L et al. Experimental realization of a quantum algorithm. Nature, 1998, 393: 143-146.
[14] Duan L M, Guo G C. Probabilistic Cloning and identification of linearly independent quantum states. Phys. Rev. Lett., 1998, 80(22): 4999-5002.
[15] Duan L M, Guo G C. Quantum error avoiding codes verses quantum error correcting codes. Phys. Lett. A, 1999, 255(4-6): 209-212.
[16] Duan L M, Guo G C. Scheme for reducing collective decoherence in quantum memory, Phys. Lett. A, 1998, 243(5-6): 265-269.
[17] 张永德等．量子信息论：物理原理和某些进展．武汉：华中师范大学出版社，2002．
[18] Wootters W K, Zurek W H. A single quantum cannot be cloned. Nature, 1982, 299: 802-803.
[19] 龙桂鲁等．量子纠缠及其在量子信息中的应用．见：曾谨言，裴寿铺，龙桂鲁编．量子力学新进展(第二辑)，北京：北京大学出版社，2001：189-259．
[20] Greenberger D M, Horne M A and Zeilinger A. In Bell' s theorem, Quantum theory, and Conceptions of the universe, edited by Kafatos M, Dordredit: Klumwer, 1989.
[21] Eisert J, Briegel H J. The Schmidt Measure as a Tool for Quantifying Multi-Particle Entanglement. Phys. Rev. A, 2001, 64(2): 022306-4.
[22] 陈增兵等．量子纠缠与空间非定域性．见：曾谨言，裴寿镛，龙桂鲁编．量子力学新进展(第二辑)，北京：北京大学出版社，2001：260-322．
[23] 张永德．量子信息物理原理．北京：科学出版社，2005．
[24] Werner R. Quantum states with Einstein-Podolosky-Rosen correlation admitting a hiden-variable model. Phys. Rev. A, 1989, 40(8): 4277-4281.
[25] Shih Y H, Alley C O. New type of Einstein-Podolsky-Rosen experiment using pairs of light quanta produced by optical parametric down-conversion. Phys. Rev. Lett., 1987, 61(26): 2921-2924.
[26] Chuang I L, Gershenfeld N, Kubinec M Get al. Bulk quantum computation with nuclear magnetic resonance: theory and experiment. Proc. R. Soc. Lond. A, 1998, 454: 447-467.
[27] Arnesen M C, Bose S, Vedral V. Natural Thermal and Magnetic Entanglement in 1D Heisenberg Model. Phys. Rev. Lett., 2001, 87(1): 017901-4.
[28] Davidovich L, Zagury N, Brune M et al. Teleportation of an atomic state between two cavities using non-local microwave fields. Phys. Rev. A, 1994, 50(2): R895-R898.
[29] Cirac J I, Parkins A S. Schemes for atomic-state teleportation. Phys. Rev. A, 1994, 50(6): R4441-R4444.
[30] Shnirman A, Schon G, Hermon Z. Quantum manipulations of small Josephson junctions. Phys. Rev. Lett., 1997, 79(12): 2371-2374.
[31] Liu Y X, Ozdemir S K, Koashi M et al. Dynamics of entanglement for coherent excitonic states in a system of two coupled quantum dots and cavity QED. Phys. Rev. A, 2002, 65(4):042326-7.
[32] Wang X G, Feng M. Barry C Sanders Multipartite entangled states in coupled quantum dots and cavity-QED. Phys. Rev. A, 2003, 67(2):022302-8.
[33] 杨洁．量子主方程及其求解的若干方法：(硕士学位论文)．合肥：中国科学技术大学，2003．
[34] von Neumann J. Mathematical Foundations of Quantum Mechanics. Princeton: Princeton Univer-sity Press, 1955.
[35] Collett M J. Exact density-matrix calculations for simple open systems. Phys. Rev. A, 1988, 38(5): 2233-2247.
[36] Dum R, Zoller P. Monte Carlo simulation of the atomic master equation for spontaneous emission. Phys. Rev. A, 1992, 45(7): 4879-4887.
[37] Mandel L, Wolf E. Optical Coherence and Quantum Optics. Cambridge: Cambridge Univ. Press, 1995.
[38] Gardiner C W, Zoller P. Quantum kinetic theory: A quantum kinetic master equation for condensation of a weakly interacting Bose gas without a trapping potential. Phys. Rev. A, 1997, 55(4): 2902-2921.
[39] Marsh J S. Explicit measurement theory for quantum mechanics. Phys. Rev. A, 2001, 64(4): 042109-15.
[40] Zanardi P. Dissipation and decoherence in a quantum register .Phys. Rev. A, 1998, 57(5): 3276-3284.
[41] Bacon D, Lidar D A, Whaley K B. Robustness of decoherence-free subspaces for quantum computation. Phys. Rev. A, 1999, 60(3): 1944-1955.
[42] Hiroshima T. Decoherence and entanglement in two-mode squeezed vacuum states. Phys. Rev. A, 2001, 63(2): 022305-4.
[43] Yu T, Eberly J H. Phonon decoherence of quantum entanglement: Robust and fragile states. Phys. Rev. B, 2002, 66(19): 193306-4.
[44] Preskill J. Lecture Notes for Physics 229: Quantum Information and Computation. CIT, 1998.
[45] Zwanzig R. Statistical Mechanics of Irreversibility, New York: Interscience, 1961.
[46] Prigogine I. Non-equilibrium Statistical Mechanics. New York: Interscience, 1962.
[47] Agarwal G S. Progress in Optics, Amsterdam: North-Holland, 1973.
[48] 路易塞尔W H著．陈水，于熙令译．辐射的量子统计性质．北京：科学出版社，1982．
[49] 韩丽萍．非线性谐振子退相干的研究：(硕士学位论文)．大连：大连理工大学，2006．
[50] Gell-Mamm M, Hartle J B. Classical equations for quantum systems. Phys. Rev. D, 1993, 47(8): 3345-3382.
[51] Walls D F, Milburn G J. Quantum Optics. Berlin: Springer-Verlag, 1994.
[52] Elze H T. Quantum decoherence, entropy and thermalization in strong interactions at high energy. (Ⅰ). Noisy and dissipative vacuum effects in toy models*1. Nucl. Phys. B, 1995, 436(1-2): 213-261.
[53] Zurek W H. Environment-induced superselection rules. Phys. Rev. D, 1982, 26(8): 1862-1880.
[54] Walls D F, Collet M J, Milburn G J. Analysis of a quantum measurement . Phys. Rev. D, 1985, 32(12): 3208-3215.
[55] Unruh W G. Maintaining coherence in quantum computers. Phys. Rev. A, 1995, 51(2): 992-997.
[56] Chaturvedi S, Srinivasan V. Solution of the master equation for an attenuated or amplified nonlinear oscillator with an arbitrary initial condition. J. Mod. Opt., 1991, 38(4): 777-783.
[57] Ban M. Lie-algebra methods in quantum optics: The Liouville-space formulation. Phys. Rev. A, 1993, 47(6): 5093-5119.
[58] Ban M. SU(1,1) Lie algebraic approach to linear dissipative processes in quantum optics. J. Math. Phys., 1992, 33(9): 3213-3228.
[59] d'Ariano G M. A group-theoretical approach to the quantum damped oscillator. Phys. Lett. A, 1994, 187(3): 231-235.
[60] Venugopalan A. Pointer states via decoherence in a quantum measurement. Phys. Rev. A, 2000, 61(1): 012102-8.
[61] Yi X X, Li C, Su J C. Perturbative expansion for the master equation and its applications. Phys. Rev. A, 2000, 62(1):013819-7.
[62] Gardiner C W. Quantum noise. New York: springer, 1991.
[63] Louisell W H, Quantum statistical properties of radiation, New York: Wiley, 1973.
[64] Van Kampen N G. Elimination of fast variables. Phys. Rep., 1985, 124(2): 69-160.
[65] Ren W, Carmichael H J. Spontaneous emission in a standing-wave cavity: Quantum-mechanical center-of-mass motion. Phys. Rev. A, 1995, 51(1): 752-773.
[66] Meystre P. Theoretical developments in cavity quantum optics: a brief review. Phys. Rep., 1992, 219(3-6): 243-262.
[67] Vernooy D W, Furusawa A, Georgiades N Pet al. Cavity QED with high-Q whispering gallery modes. Phys. Rev. A, 1998, 57(4), R2293-R2296.
[68] Kim M S, Antesberger G, Bodendorf C T et al. Scheme for direct observation of the Wigner characteristic function in cavity QED. Phys. Rev. A, 1998, 58(1): R65-R68 .
[69] Haroche S, Kleppner D. Cavity quantum electrodynamics. Phys. Today, 1989, 42(1): 24-30.
[70] Yi X X, Yu S X. Effective Hamiltonian approach to the master equation. J. Opt. B, 2001, 3(1): 372-375.
[71] Nambu Y. On the Method of the Third Quantization. Prog. Theor. Phys., 1949, 4(3): 331-346.
[72] Fano U. Description of States in Quantum Mechanics by Density Matrix and Operator Techniques. Rev. Mod. Phys., 1957, 29(1): 74-93.
[73] 尼尔森M A著．郑大钟，赵千川译．量子计算和量子信息(二)—量子信息部分．北京：清华大学出版社．2004．
[74] 曾谨言，裴寿镐．纠缠态．见：曾谨言，裴寿镛编．量子力学新进展(第一辑)．北京：北京大学出版社，2000：1-45．
[75] 张礼，葛墨林．量子力学的前沿问题．北京：清华大学出版社，2000．
[76] 杨伯君．量子光学基础．北京：北京邮电大学出版社，1996．
[77] 彭金生，李高翔．近代量子光学导论．北京：科学出版社，1996．
[78] 李承祖，黄明球，陈平形等．量子通信与量子计算．长沙：国防科技大学出版社，2000．
[79] 张镇九，张昭理，李爱民．量子计算和通信加密．武汉：华中师范大学出版社，2002．
[80] Zurek W H. Decoherence and the Transition from Quantum to Classical. Phys. Today, 1991, 44(10): 36-44.
[81] Haroche S. Entanglement, decoherence and the quantum/classical boundary. Phys. Today, 1998, 51(7): 36-42.
[82] 孙昌璞，衣学喜，周端陆等．量子退相干问题．见：曾谨言，裴寿墉编．量子力学新进展(第一辑)．北京：北京大学出版社，2000：59-130．
[83] 曾谨言．量子力学卷Ⅱ．北京：科学出版社，2000．
[84] Nielsen M A, Chuang I L. Quantum Computation and Quantum Information. Cambridge: Cambridge University Press, 2000.
[85] Plenio M B, Vedral V. Entanglement in Quantum Information Theory. Contemp. Phys., 1998, 39: 431-466.
[86] 尼尔森M A著．赵千川译．量子计算和量子信息(一)—量子计算部分．北京：清华大学出版社，2004．
[87] Bennett C H, Divincenzo D P. Quantum information and computation. Nature, 2000, 404: 247-255.
[88] Preskill J. Reliable Quantum Computers. Proc. R. Soc. A, 1998, 454: 385-410.
[89] Zanardi P. Stabilizing quantum information. Phys. Rev. A, 2001, 63(1): 012301-4.
[90] Kielpinski D, Meyer V, Rowe M A et al. A Decoherence-Free Quantum Memory Using Trapped Ions. Science, 2001, 291: 1013-1015.
[91] Kwiat P G, Berglund A J, Altepeter J B et al. Experimental Verification of Decoherence-Free Subspaces. Science, 2000, 290: 498-501.
[92] Cabrillo C, Cirac J I, Garcia-Fernandez P et al. Creation of entangled states of distant atoms by interference. Phys. Rev. A, 1999, 59(2): I025-I033.
[93] Plenio M B, Huelga S F, Beige A et al. Cavity-loss-induced generation of entangled atoms. Phys. Rev. A, 1999, 59(3): 2468-2475.
[94] Beige A, Bose S, Braun D et al. Entanglement atoms and ions in dissipative environments. J. Mod. Opt., 2000, 47(14-15): 2583-2598.
[95] Horodecki P. "Interaction-free" interaction: Entangling evolution coming from the possibility of detection. Phys. Rev. A, 2001, 63(2): 022108-6.
[96] Schneider S, Milburn G J. Entanglement in the steady state of a collective- angular-momentum (Dicke) model. Phys. Rev. A, 2002, 65(4): 042107-6.
[97] Kim M S, Lee J, Ahn D et al. Entanglement induced by a single-mode heat environment. Phys. Rev. A, 2002, 65(4): 040101-4.
[98] Kraus B, Cirac J I. Discrete Entanglement Distribution with Squeezed Light. Phys. Rev. Lett., 2004, 92(1): 013602-4.
[99] Duan L M, Kimble H J. Efficient Engineering of Multiatom Entanglement through Single-Photon Detections. Phys. Rev. Lett., 2003, 90(25): 253601-4.
[100] 常俊丽．关于量子噪声和复合系统非对角几何相的研究：(硕士学位论文)．大连：大连理工大学，2006．
[101] Walls D F, Milburn G J. Effect of dissipation on quantum coherence. Phys. Rev. A, 1985, 31(4): 2403-2408.
[102] Quang T, Knight P L, Buek V. Quantum collapses and revivals in an optical cavity. Phys. Rev. A, 1991, 44(9): 6092-6096.
[103] Bose S, Knight P L, Plenio M B et al. Proposal for Teleportation of an Atomic State via Cavity Decay. Phys. Rev. Lett., 1999, 83(24): 5158-5161.
[104] Plenio M B, Huelga S F. Entangled Light from White Noise. Phys. Rev. Lett., 2002, 88(19): 197901-4.
[105] Vidal G, Werner R F. Computable measure of entanglement. Phys. Rev. A, 2002, 65(3): 032314-11.
[106] Eisert J. Entanglement in Quantum Information Theory: (Ph. D thesis). Potsdam: University of Potsdam, 2001.
[107] Gammaitoni L, Hanggi P, Jung P et al. Stochastic resonance. Rev. Mod. Phys., 1998, 70(1): 223-287.
[108] Huelga S F, Plenio M B. Quantum stochastic resonance in electron shelving. Phys. Rev. A, 2000, 62(5): 052111-4.
[109] Buchleitner A, Mantegna R N. Quantum Stochastic Resonance in a Micromaser. Phys. Rev. Lett., 1998, 80(18): 3932-3935.
[110] Yi X X, Yu C S, Zhou L et al. Noise-assisted preparation of entangled atoms. Phys. Rev. A, 2003, 68(5): 052304-4.
[111] Gardiner C W, Zoller P. Quantum Noise. New York: Springer. 2000.
[112] Puri R R. Mathematical methods of quantum optics. Berlin: Springer, 2001.
[113] Wootters W K. Entanglement of Formation of Arbitrary State of Two Qubits. Phys. Rev. Lett., 1998, 80(10): 2245-2248.
[114] Hill S, Wooters W K. Entanglement of a Pair of Quantum Bits. Phys. Rev. Lett., 1997, 78(26): 5022-5025.
[115] Horodecki M, Horodecki P. Reduction criterion of separability and limits for a class of distillation protocols. Phys. Rev. A, 1999, 59(6): 4206-4216.
[116] Yi X X, Guo G C. All-optical electron spin quantum computer with ancilla bits for operations in each coupled-dot cell. Phys. Rev. A, 2000, 62(6): 062312-6.
[117] Chen J, Yi X X, Song H S et al. Noise Induced Entanglement. International Journal of Quantum Information, 2005, 3(2): 425-433.
[118] Gardiner C W. Inhibition of Atomic Phase Decays by Squeezed Light: A Direct Effect of Squeezing. Phys. Rev. Lett., 1986, 56(18): 1917-1920.
[119] Clark S, Parkins S. Coupling of effective one-dimensional two-level atoms to squeezed light. J. Opt. B, 2003, 5(2): 145-154.
[120] Georgiades N Ph, Polzik E S, Edamatsu K et al. Nonclassical Excitation for Atoms in a Squeezed Vacuum. Phys. Rev. Lett., 1995, 75(19): 3426-3429.
[121] Long G L, Ma Y J, Chen H M. An Electron-Nucleon Double Spin Solid-State Quantum Computer. Chinese Journal of Semiconductors, 2003, 24(Supplement): 43-46.
[122] Chang J L, Wang L C, Chen J et al. Steady State Atom-Photon Entanglement in Cavity QED Systems. Chin. J. Phys., 2005, 43(6): 1074-1082.
[123] Law C K, Kimble H J. Deterministic generation of bit-stream of single-photon pulses. J. Mod. Opt., 1997, 44(11-12): 2067-2074.
[124] Eberly J, Law C K. CLASSICAL CONTROL OF QUANTIZED FIELDS: CAVITY QED AND THE PHOTON PISTOL. Acta. Phys. Pol. A, 1998, 93(1): 55-62.
[125] Sun B, Chapman M S, You L. Atom-photon entanglement generation and distribution. Phys. Rev. A, 2004, 69(4): 042316-6.
[126] Rempe G, Schmidt-Kaler F, Walther H. Observation of sub-Poissonian photon statistics in a micromaser. Phys. Rev. Lett., 1990, 64(23): 2783-2786.
[127] Rempe G, Thompson R J, Brecha R J et al. Optical bistability and photon statistics in cavity quantum electrodynamics. Phys. Rev. Lett., 1991, 67(13): 1727-1730.
[128] Brune M, Schmidt-Kaler F, Maali A et al. Quantum Rabi Oscillation: A Direct Test of Field Quantization in a Cavity. Phys. Rev. Lett., 1996, 76(11): 1800-1803.
[129] Childs J J, An K, Otteson M S et al. Normal-Mode Line Shapes for Atoms in Standing-Wave Optical Resonators. Phys. Rev. Lett., 1996, 77(14): 2901-2904.
[130] Kuhn A, Hennrich M, Bondo T et al. Controlled generation of single photon from a strongly coupled atom-cavity system. Appl. Phys. B: Lasers Opt., 1999, 69(5-6): 373-377.
[131] Nha H, Chough Y T, An K. Single-photon state in a driven Jaynes-Cummings system. Phys. Rev. A, 2001, 63(1): 010301-4.
[132] Anderson B P, Kasevich M A. Macroscopic Quantum Interference from Atomic Tunnel Arrays. Science, 1998, 282(5394): 1686-1689.
[133] Cataliotti F S, Burger S, Fort C et al. Josephson Junction Arrays with Bose-Einstein Condensates . Science, 2001,293(5531): 843-846.
[134] Smerzi A, Fantoni S, Giovanazzi S et al. Quantum Coherent Atomic Tunneling between Two Trapped Bose-Einstein Condensates. Phys. Rev. Lett., 1997, 79(25): 4950-4953.
[135] Milburn G J, Corney J, Wright E M et al. Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential . Phys. Rev. A, 1997, 55(6): 4318-4324.
[136] Raghavan S, Smerzi A, Fantoni S et al. Coherent oscillations between two weakly coupled Bose- Einstein condensates: Josephson effects, π oscillations and macroscopic quantum self-trapping. Phys. Rev. A, 1999, 59(1): 620-633.
[137] Williams J E. Optimal conditions for observing Josephson oscillations in a double-well Bose-Einstein condensate. Phys. Rev. A, 2001, 64(1): 013610-7.
[138] Ng H T, Law C K, Leung P T. Quantum-correlated double-well tunneling of two-component Bose-Einstein condensates. Phys. Rev. A, 2003, 68(1): 013604-6.
[139] Imamoglu A, Lewenstein M, You L. Inhibition of Coherence in Trapped Bose-Einstein Condensates. Phys. Rev. Lett., 1997, 78(13): 2511-2514.
[140] Javanainen J, Ivanov M Y. Splitting a trap containing a Bose-Einstein condensate: Atom number fluctuations. Phys. Rev. A, 1999, 60(3): 2351-2359.
[141] Peres A. Quantum Theory: Concepts and Methods. Dordrecht: Kluwer Academic, 1995.
[142] Hines A P, McKenzie R H, Milburn G J. Entanglement of two-mode Bose-Einstein condensates. Phys. Rev. A, 2003, 67(1): 013609-10.
[143] Anglin J R, Ketterle W. Bose-Einstein condensation of atomic gases . Nature, 2002, 416: 211-218.
[144] Micheli A, Jaksch D, Cirac J I et al. Many particle entanglement in two-component Bose-Einstein Condensates, cond-mat/0205369.
[145] You L. Creating Maximally Entangled Atomic States in a Bose-Einstein Condensate. Phys. Rev. Lett., 2003, 90(3): 030402-4.
[146] Leggett A J. Bose-Einstein condensation in the alkali gases: Some fundamental concepts. Rev. Mod. Phys., 2001, 73(2): 307-356.
[147] Mahmud K W, Perry H, Reinhardt W P. Quantum phase-space picture of Bose-Einstein condensates in a double well. Phys. Rev. A, 2005, 71: 023615-17.
[148] Lee H. Theory and application of the quantum phase-space distribution functions. Phys. Rep., 1995, 259(1): 147-211.
[149] Greenberger D M, Home M A, Shimony A et al. Bell's theorem without inequalities. Am. J. Phys., 1990, 58(12): 1131-1143.
[150] Bell J S. Speakable and Unspeakable in Quantum Mechanics. New York: Cambridge University Press, 1987.
[151] Chen J, Guo Y Q, Cao H J et al. Two-mode entanglement using a spin-1/2 approximation method in two-component condensates. Phys. Lett. A., 2007, 360(3): 429-434.
[152] Spekkens R W, Sipe J E. Spatial fragmentation of a Bose-Einstein condensate in a double-well potential. Phys. Rev. A, 1999, 59(5): 3868-3877.
[153] Reinhardt W P, Perry H. Fundamental World in Quantum Chemistry, edited by Brandas E J and Kryachko E S. Dordrecht: Kluwer, 2003.
[154] Myatt C J, Burt E A, Ghrist R W et al. Production of Two Overlapping Bose-Einstein Condensates by Sympathetic Cooling. Phys. Rev. Lett., 1997, 78(4): 586-589.
[155] Anglin J R, Drummond P, Smerzi A. Exact quantum phase model for mesoscopic Josephson junctions. Phys. Rev. A, 2001, 64(6): 063605-4.
[156] Bandyopadhyay A, Rai J. Uncertainties of Schwinger angular-momentum operators for squeezed radiation in interferometers. Phys. Rev. A, 1995, 51(2): 1597-1603.
[157] Hall D S, Matthews M R, Ensher J R et al. Dynamics of Component Separation in a Binary Mixture of Bose-Einstein Condensates. Phys. Rev. Lett., 1998, 81(8): 1539-1542.
[158] Law C K, Ng H T, Leung P T. Coherent control of spin squeezing. Phys. Rev. A, 2001, 63(5): 055601-3.
[159] Modugno G, Modugno M, Riboli F et al. Two Atomic Species Superfluid. Phys. Rev. Lett., 2002, 89(19): 190404-4.
[160] Chen J, Yu C S, Song H S. Elementary Quantum Gates Based on Intrinsic Interaction Hamiltonian. Commun. Theor. Phys., 2006, 46(1): 69-72.
[161] Barenco A, Bennett C H, Cleve R et al. Elementary gates for quantum computation. Phys. Rev. A, 1995, 52(5): 3457-3467.
[162] Shi Y. Both Toffoli and Controlled-NOT need little help to do universal quantum computation. quant-ph/0205115.
[163] Fredkin E, Toffoli T. Conservation logic. Internat. J. Theoret. phys., 1982, 21: 219-253.
[164] Toffoli T. Reversible Computing, in Automata, languages and Programming, eds, de Bakker J W and Van Leeuwer J. New York: Sping, 1980.
[165] Zhu S L, Wang Z D. Universal quantum gates based on a pair of orthogonal cyclic states: Application to NMR systems. Phys. Rev. A, 2003, 67(2): 022319-9.
[166] DiVincenzo D P. The Physical Implementation of Quantum Computation. Fortschr. Phys., 2000,48: 771-783.
[167] Harrow A W, Nielsen M A. Robustness of quantum gates in the presence of noise. Phys. Rev. A, 2003, 68(1): 012308-13.
[168] Cirac J I, Zoller P. Quantum Computations with Cold Trapped Ions. Phys. Rev. Lett., 1995, 74(20): 4091-4094.
[169] Pellizzari T, Gardiner S A, Cirac J I et al. Decoherence, Continuous Observation, and Quantum Computing: A Cavity QED Model. Phys. Rev. Lett., 1995, 75(21): 3788-3791.
[170] Gershenfeld N A, Chuang I L. Bulk Spin-Resonance Quantum Computation. Science, 1997, 275(5298): 350-356.
[171] Makhlin Y, Schon G, Shnirman A. Quantum-state engineering with Josephson-junction devices. Rev. Mod. Phys., 2001, 73(2): 357-400.
[172] Nakamura Y, Pashkin Y A, Tsai J S. Coherent control of macroscopic quantum states in a single- Cooper-pair box. Nature, 1999, 398: 786-788.
[173] Falci G, Fazio R, Palma G M et al. Detection of geometric phases in superconducting nanocircuits. Nature, 2000, 407: 355-358.
[174] Bacon D, Kempe J, DiVincenzo D P et al. Encoded Universality in Physical Implementations of a Quantum Computer, quant-ph/0102140.
[175] Preskill J. Lecture Notes for Physics 229: Quantum Information and Computation, California: California Institute of Technology, 1998.
[176] Mollow B R, Glauber R J. Quantum Theory of Parametric Amplification. I. Phys. Rev., 1967, 160(5): 1076-1096.
[177] Mollow B R. Quantum Statistics of Coupled Oscillator Systems. Phys. Rev., 1967, 162(5): 1256- 1273.
[178] Reid M D, Walls D F. Violations of classical inequalities in quantum optics. Phys. Rev. A, 1986, 34(2): 1260-1276.
[179] Anderson P W. Limits on the Energy of the Antiferromagnetic Ground State. Phys. Rev., 1951, 83(6): 1260-1260.
[180] Deutsch D. Universality in quantum computation. Proc. Roy. Soc. London Ser. A, 1995, 449: 669-677.
[181] Lloyd S. Almost Any Quantum Logic Gate is Universal. Phys. Rev. Lett., 1995, 75(2): 346-349.
[182] Deutsch D. Quantum computational networks. Proc. Roy. Soc. London Ser. A, 1989, 425: 73-90.
[183] Barenco A. A universal two-bit gate for quantum computation. Proc. Roy. Soc. London Ser. A, 1995, 449: 679-683. Notation: quant-ph/, cond-mat/ please see http://Arxiv.org/abs/xx-xx/xxxxxxx.
[2] 李崇．量子通讯理论的矩阵表述：(博士学位论文)．大连：大连理工大学，2003．
[3] Einstein A, Podolsky B, Rosen N. Can Quantum-Mechanical Description of Physical Reality Be Considerd Complete? Phys. Rev., 1935, 47(10): 777-780.
[4] 宋鹤山．量子力学．大连：大连理工大学出版社，2004．
[5] Bennett C H, Brassard G. Quantum cryptography: public key distribution and coin tossing. Proc. IEEE Int. Conf. On Computers, Systems and Signal Processing, Bangalore, India (IEEE, New York), 1984, p175-179.
[6] Bennett C H. Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett., 1992, 68(21): 3121-3124.
[7] Hiskett P A, Rosenberg D, Peterson C G et al. Long-distance quantum key distribution in optical fibre. New Journal of Physics, 2006, 8: 193-196.
[8] Bennett C H, Brassard G, Crepeau C et al. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett., 1993, 70(13): 1895-1899.
[9] Bouwmeester D, Pan J W, Matle K et al. Experimental quantum teleportation. Nature, 1997, 390: 575-579.
[10] 张永德．综述：漫谈量子信息学．北京：人民日报，2003．
[11] Shor P W, Polynomial-Time algorithms for prime factorization and discrete logarithms on a quantum computer, Proceedings of the 35th Annual Symposium on Foundations of computer Science, Santa Fe NM: IEEE Computer Society Press, 1994, 20: 124-134.
[12] Grover L K. Quantum Mechanics Helps in searching for a Needle in a Haystack, Phys. Rev. Lett., 1997, 79(2): 325-328.
[13] Chuang I L, Vandersypen L M K, Zhou X L et al. Experimental realization of a quantum algorithm. Nature, 1998, 393: 143-146.
[14] Duan L M, Guo G C. Probabilistic Cloning and identification of linearly independent quantum states. Phys. Rev. Lett., 1998, 80(22): 4999-5002.
[15] Duan L M, Guo G C. Quantum error avoiding codes verses quantum error correcting codes. Phys. Lett. A, 1999, 255(4-6): 209-212.
[16] Duan L M, Guo G C. Scheme for reducing collective decoherence in quantum memory, Phys. Lett. A, 1998, 243(5-6): 265-269.
[17] 张永德等．量子信息论：物理原理和某些进展．武汉：华中师范大学出版社，2002．
[18] Wootters W K, Zurek W H. A single quantum cannot be cloned. Nature, 1982, 299: 802-803.
[19] 龙桂鲁等．量子纠缠及其在量子信息中的应用．见：曾谨言，裴寿铺，龙桂鲁编．量子力学新进展(第二辑)，北京：北京大学出版社，2001：189-259．
[20] Greenberger D M, Horne M A and Zeilinger A. In Bell' s theorem, Quantum theory, and Conceptions of the universe, edited by Kafatos M, Dordredit: Klumwer, 1989.
[21] Eisert J, Briegel H J. The Schmidt Measure as a Tool for Quantifying Multi-Particle Entanglement. Phys. Rev. A, 2001, 64(2): 022306-4.
[22] 陈增兵等．量子纠缠与空间非定域性．见：曾谨言，裴寿镛，龙桂鲁编．量子力学新进展(第二辑)，北京：北京大学出版社，2001：260-322．
[23] 张永德．量子信息物理原理．北京：科学出版社，2005．
[24] Werner R. Quantum states with Einstein-Podolosky-Rosen correlation admitting a hiden-variable model. Phys. Rev. A, 1989, 40(8): 4277-4281.
[25] Shih Y H, Alley C O. New type of Einstein-Podolsky-Rosen experiment using pairs of light quanta produced by optical parametric down-conversion. Phys. Rev. Lett., 1987, 61(26): 2921-2924.
[26] Chuang I L, Gershenfeld N, Kubinec M Get al. Bulk quantum computation with nuclear magnetic resonance: theory and experiment. Proc. R. Soc. Lond. A, 1998, 454: 447-467.
[27] Arnesen M C, Bose S, Vedral V. Natural Thermal and Magnetic Entanglement in 1D Heisenberg Model. Phys. Rev. Lett., 2001, 87(1): 017901-4.
[28] Davidovich L, Zagury N, Brune M et al. Teleportation of an atomic state between two cavities using non-local microwave fields. Phys. Rev. A, 1994, 50(2): R895-R898.
[29] Cirac J I, Parkins A S. Schemes for atomic-state teleportation. Phys. Rev. A, 1994, 50(6): R4441-R4444.
[30] Shnirman A, Schon G, Hermon Z. Quantum manipulations of small Josephson junctions. Phys. Rev. Lett., 1997, 79(12): 2371-2374.
[31] Liu Y X, Ozdemir S K, Koashi M et al. Dynamics of entanglement for coherent excitonic states in a system of two coupled quantum dots and cavity QED. Phys. Rev. A, 2002, 65(4):042326-7.
[32] Wang X G, Feng M. Barry C Sanders Multipartite entangled states in coupled quantum dots and cavity-QED. Phys. Rev. A, 2003, 67(2):022302-8.
[33] 杨洁．量子主方程及其求解的若干方法：(硕士学位论文)．合肥：中国科学技术大学，2003．
[34] von Neumann J. Mathematical Foundations of Quantum Mechanics. Princeton: Princeton Univer-sity Press, 1955.
[35] Collett M J. Exact density-matrix calculations for simple open systems. Phys. Rev. A, 1988, 38(5): 2233-2247.
[36] Dum R, Zoller P. Monte Carlo simulation of the atomic master equation for spontaneous emission. Phys. Rev. A, 1992, 45(7): 4879-4887.
[37] Mandel L, Wolf E. Optical Coherence and Quantum Optics. Cambridge: Cambridge Univ. Press, 1995.
[38] Gardiner C W, Zoller P. Quantum kinetic theory: A quantum kinetic master equation for condensation of a weakly interacting Bose gas without a trapping potential. Phys. Rev. A, 1997, 55(4): 2902-2921.
[39] Marsh J S. Explicit measurement theory for quantum mechanics. Phys. Rev. A, 2001, 64(4): 042109-15.
[40] Zanardi P. Dissipation and decoherence in a quantum register .Phys. Rev. A, 1998, 57(5): 3276-3284.
[41] Bacon D, Lidar D A, Whaley K B. Robustness of decoherence-free subspaces for quantum computation. Phys. Rev. A, 1999, 60(3): 1944-1955.
[42] Hiroshima T. Decoherence and entanglement in two-mode squeezed vacuum states. Phys. Rev. A, 2001, 63(2): 022305-4.
[43] Yu T, Eberly J H. Phonon decoherence of quantum entanglement: Robust and fragile states. Phys. Rev. B, 2002, 66(19): 193306-4.
[44] Preskill J. Lecture Notes for Physics 229: Quantum Information and Computation. CIT, 1998.
[45] Zwanzig R. Statistical Mechanics of Irreversibility, New York: Interscience, 1961.
[46] Prigogine I. Non-equilibrium Statistical Mechanics. New York: Interscience, 1962.
[47] Agarwal G S. Progress in Optics, Amsterdam: North-Holland, 1973.
[48] 路易塞尔W H著．陈水，于熙令译．辐射的量子统计性质．北京：科学出版社，1982．
[49] 韩丽萍．非线性谐振子退相干的研究：(硕士学位论文)．大连：大连理工大学，2006．
[50] Gell-Mamm M, Hartle J B. Classical equations for quantum systems. Phys. Rev. D, 1993, 47(8): 3345-3382.
[51] Walls D F, Milburn G J. Quantum Optics. Berlin: Springer-Verlag, 1994.
[52] Elze H T. Quantum decoherence, entropy and thermalization in strong interactions at high energy. (Ⅰ). Noisy and dissipative vacuum effects in toy models*1. Nucl. Phys. B, 1995, 436(1-2): 213-261.
[53] Zurek W H. Environment-induced superselection rules. Phys. Rev. D, 1982, 26(8): 1862-1880.
[54] Walls D F, Collet M J, Milburn G J. Analysis of a quantum measurement . Phys. Rev. D, 1985, 32(12): 3208-3215.
[55] Unruh W G. Maintaining coherence in quantum computers. Phys. Rev. A, 1995, 51(2): 992-997.
[56] Chaturvedi S, Srinivasan V. Solution of the master equation for an attenuated or amplified nonlinear oscillator with an arbitrary initial condition. J. Mod. Opt., 1991, 38(4): 777-783.
[57] Ban M. Lie-algebra methods in quantum optics: The Liouville-space formulation. Phys. Rev. A, 1993, 47(6): 5093-5119.
[58] Ban M. SU(1,1) Lie algebraic approach to linear dissipative processes in quantum optics. J. Math. Phys., 1992, 33(9): 3213-3228.
[59] d'Ariano G M. A group-theoretical approach to the quantum damped oscillator. Phys. Lett. A, 1994, 187(3): 231-235.
[60] Venugopalan A. Pointer states via decoherence in a quantum measurement. Phys. Rev. A, 2000, 61(1): 012102-8.
[61] Yi X X, Li C, Su J C. Perturbative expansion for the master equation and its applications. Phys. Rev. A, 2000, 62(1):013819-7.
[62] Gardiner C W. Quantum noise. New York: springer, 1991.
[63] Louisell W H, Quantum statistical properties of radiation, New York: Wiley, 1973.
[64] Van Kampen N G. Elimination of fast variables. Phys. Rep., 1985, 124(2): 69-160.
[65] Ren W, Carmichael H J. Spontaneous emission in a standing-wave cavity: Quantum-mechanical center-of-mass motion. Phys. Rev. A, 1995, 51(1): 752-773.
[66] Meystre P. Theoretical developments in cavity quantum optics: a brief review. Phys. Rep., 1992, 219(3-6): 243-262.
[67] Vernooy D W, Furusawa A, Georgiades N Pet al. Cavity QED with high-Q whispering gallery modes. Phys. Rev. A, 1998, 57(4), R2293-R2296.
[68] Kim M S, Antesberger G, Bodendorf C T et al. Scheme for direct observation of the Wigner characteristic function in cavity QED. Phys. Rev. A, 1998, 58(1): R65-R68 .
[69] Haroche S, Kleppner D. Cavity quantum electrodynamics. Phys. Today, 1989, 42(1): 24-30.
[70] Yi X X, Yu S X. Effective Hamiltonian approach to the master equation. J. Opt. B, 2001, 3(1): 372-375.
[71] Nambu Y. On the Method of the Third Quantization. Prog. Theor. Phys., 1949, 4(3): 331-346.
[72] Fano U. Description of States in Quantum Mechanics by Density Matrix and Operator Techniques. Rev. Mod. Phys., 1957, 29(1): 74-93.
[73] 尼尔森M A著．郑大钟，赵千川译．量子计算和量子信息(二)—量子信息部分．北京：清华大学出版社．2004．
[74] 曾谨言，裴寿镐．纠缠态．见：曾谨言，裴寿镛编．量子力学新进展(第一辑)．北京：北京大学出版社，2000：1-45．
[75] 张礼，葛墨林．量子力学的前沿问题．北京：清华大学出版社，2000．
[76] 杨伯君．量子光学基础．北京：北京邮电大学出版社，1996．
[77] 彭金生，李高翔．近代量子光学导论．北京：科学出版社，1996．
[78] 李承祖，黄明球，陈平形等．量子通信与量子计算．长沙：国防科技大学出版社，2000．
[79] 张镇九，张昭理，李爱民．量子计算和通信加密．武汉：华中师范大学出版社，2002．
[80] Zurek W H. Decoherence and the Transition from Quantum to Classical. Phys. Today, 1991, 44(10): 36-44.
[81] Haroche S. Entanglement, decoherence and the quantum/classical boundary. Phys. Today, 1998, 51(7): 36-42.
[82] 孙昌璞，衣学喜，周端陆等．量子退相干问题．见：曾谨言，裴寿墉编．量子力学新进展(第一辑)．北京：北京大学出版社，2000：59-130．
[83] 曾谨言．量子力学卷Ⅱ．北京：科学出版社，2000．
[84] Nielsen M A, Chuang I L. Quantum Computation and Quantum Information. Cambridge: Cambridge University Press, 2000.
[85] Plenio M B, Vedral V. Entanglement in Quantum Information Theory. Contemp. Phys., 1998, 39: 431-466.
[86] 尼尔森M A著．赵千川译．量子计算和量子信息(一)—量子计算部分．北京：清华大学出版社，2004．
[87] Bennett C H, Divincenzo D P. Quantum information and computation. Nature, 2000, 404: 247-255.
[88] Preskill J. Reliable Quantum Computers. Proc. R. Soc. A, 1998, 454: 385-410.
[89] Zanardi P. Stabilizing quantum information. Phys. Rev. A, 2001, 63(1): 012301-4.
[90] Kielpinski D, Meyer V, Rowe M A et al. A Decoherence-Free Quantum Memory Using Trapped Ions. Science, 2001, 291: 1013-1015.
[91] Kwiat P G, Berglund A J, Altepeter J B et al. Experimental Verification of Decoherence-Free Subspaces. Science, 2000, 290: 498-501.
[92] Cabrillo C, Cirac J I, Garcia-Fernandez P et al. Creation of entangled states of distant atoms by interference. Phys. Rev. A, 1999, 59(2): I025-I033.
[93] Plenio M B, Huelga S F, Beige A et al. Cavity-loss-induced generation of entangled atoms. Phys. Rev. A, 1999, 59(3): 2468-2475.
[94] Beige A, Bose S, Braun D et al. Entanglement atoms and ions in dissipative environments. J. Mod. Opt., 2000, 47(14-15): 2583-2598.
[95] Horodecki P. "Interaction-free" interaction: Entangling evolution coming from the possibility of detection. Phys. Rev. A, 2001, 63(2): 022108-6.
[96] Schneider S, Milburn G J. Entanglement in the steady state of a collective- angular-momentum (Dicke) model. Phys. Rev. A, 2002, 65(4): 042107-6.
[97] Kim M S, Lee J, Ahn D et al. Entanglement induced by a single-mode heat environment. Phys. Rev. A, 2002, 65(4): 040101-4.
[98] Kraus B, Cirac J I. Discrete Entanglement Distribution with Squeezed Light. Phys. Rev. Lett., 2004, 92(1): 013602-4.
[99] Duan L M, Kimble H J. Efficient Engineering of Multiatom Entanglement through Single-Photon Detections. Phys. Rev. Lett., 2003, 90(25): 253601-4.
[100] 常俊丽．关于量子噪声和复合系统非对角几何相的研究：(硕士学位论文)．大连：大连理工大学，2006．
[101] Walls D F, Milburn G J. Effect of dissipation on quantum coherence. Phys. Rev. A, 1985, 31(4): 2403-2408.
[102] Quang T, Knight P L, Buek V. Quantum collapses and revivals in an optical cavity. Phys. Rev. A, 1991, 44(9): 6092-6096.
[103] Bose S, Knight P L, Plenio M B et al. Proposal for Teleportation of an Atomic State via Cavity Decay. Phys. Rev. Lett., 1999, 83(24): 5158-5161.
[104] Plenio M B, Huelga S F. Entangled Light from White Noise. Phys. Rev. Lett., 2002, 88(19): 197901-4.
[105] Vidal G, Werner R F. Computable measure of entanglement. Phys. Rev. A, 2002, 65(3): 032314-11.
[106] Eisert J. Entanglement in Quantum Information Theory: (Ph. D thesis). Potsdam: University of Potsdam, 2001.
[107] Gammaitoni L, Hanggi P, Jung P et al. Stochastic resonance. Rev. Mod. Phys., 1998, 70(1): 223-287.
[108] Huelga S F, Plenio M B. Quantum stochastic resonance in electron shelving. Phys. Rev. A, 2000, 62(5): 052111-4.
[109] Buchleitner A, Mantegna R N. Quantum Stochastic Resonance in a Micromaser. Phys. Rev. Lett., 1998, 80(18): 3932-3935.
[110] Yi X X, Yu C S, Zhou L et al. Noise-assisted preparation of entangled atoms. Phys. Rev. A, 2003, 68(5): 052304-4.
[111] Gardiner C W, Zoller P. Quantum Noise. New York: Springer. 2000.
[112] Puri R R. Mathematical methods of quantum optics. Berlin: Springer, 2001.
[113] Wootters W K. Entanglement of Formation of Arbitrary State of Two Qubits. Phys. Rev. Lett., 1998, 80(10): 2245-2248.
[114] Hill S, Wooters W K. Entanglement of a Pair of Quantum Bits. Phys. Rev. Lett., 1997, 78(26): 5022-5025.
[115] Horodecki M, Horodecki P. Reduction criterion of separability and limits for a class of distillation protocols. Phys. Rev. A, 1999, 59(6): 4206-4216.
[116] Yi X X, Guo G C. All-optical electron spin quantum computer with ancilla bits for operations in each coupled-dot cell. Phys. Rev. A, 2000, 62(6): 062312-6.
[117] Chen J, Yi X X, Song H S et al. Noise Induced Entanglement. International Journal of Quantum Information, 2005, 3(2): 425-433.
[118] Gardiner C W. Inhibition of Atomic Phase Decays by Squeezed Light: A Direct Effect of Squeezing. Phys. Rev. Lett., 1986, 56(18): 1917-1920.
[119] Clark S, Parkins S. Coupling of effective one-dimensional two-level atoms to squeezed light. J. Opt. B, 2003, 5(2): 145-154.
[120] Georgiades N Ph, Polzik E S, Edamatsu K et al. Nonclassical Excitation for Atoms in a Squeezed Vacuum. Phys. Rev. Lett., 1995, 75(19): 3426-3429.
[121] Long G L, Ma Y J, Chen H M. An Electron-Nucleon Double Spin Solid-State Quantum Computer. Chinese Journal of Semiconductors, 2003, 24(Supplement): 43-46.
[122] Chang J L, Wang L C, Chen J et al. Steady State Atom-Photon Entanglement in Cavity QED Systems. Chin. J. Phys., 2005, 43(6): 1074-1082.
[123] Law C K, Kimble H J. Deterministic generation of bit-stream of single-photon pulses. J. Mod. Opt., 1997, 44(11-12): 2067-2074.
[124] Eberly J, Law C K. CLASSICAL CONTROL OF QUANTIZED FIELDS: CAVITY QED AND THE PHOTON PISTOL. Acta. Phys. Pol. A, 1998, 93(1): 55-62.
[125] Sun B, Chapman M S, You L. Atom-photon entanglement generation and distribution. Phys. Rev. A, 2004, 69(4): 042316-6.
[126] Rempe G, Schmidt-Kaler F, Walther H. Observation of sub-Poissonian photon statistics in a micromaser. Phys. Rev. Lett., 1990, 64(23): 2783-2786.
[127] Rempe G, Thompson R J, Brecha R J et al. Optical bistability and photon statistics in cavity quantum electrodynamics. Phys. Rev. Lett., 1991, 67(13): 1727-1730.
[128] Brune M, Schmidt-Kaler F, Maali A et al. Quantum Rabi Oscillation: A Direct Test of Field Quantization in a Cavity. Phys. Rev. Lett., 1996, 76(11): 1800-1803.
[129] Childs J J, An K, Otteson M S et al. Normal-Mode Line Shapes for Atoms in Standing-Wave Optical Resonators. Phys. Rev. Lett., 1996, 77(14): 2901-2904.
[130] Kuhn A, Hennrich M, Bondo T et al. Controlled generation of single photon from a strongly coupled atom-cavity system. Appl. Phys. B: Lasers Opt., 1999, 69(5-6): 373-377.
[131] Nha H, Chough Y T, An K. Single-photon state in a driven Jaynes-Cummings system. Phys. Rev. A, 2001, 63(1): 010301-4.
[132] Anderson B P, Kasevich M A. Macroscopic Quantum Interference from Atomic Tunnel Arrays. Science, 1998, 282(5394): 1686-1689.
[133] Cataliotti F S, Burger S, Fort C et al. Josephson Junction Arrays with Bose-Einstein Condensates . Science, 2001,293(5531): 843-846.
[134] Smerzi A, Fantoni S, Giovanazzi S et al. Quantum Coherent Atomic Tunneling between Two Trapped Bose-Einstein Condensates. Phys. Rev. Lett., 1997, 79(25): 4950-4953.
[135] Milburn G J, Corney J, Wright E M et al. Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential . Phys. Rev. A, 1997, 55(6): 4318-4324.
[136] Raghavan S, Smerzi A, Fantoni S et al. Coherent oscillations between two weakly coupled Bose- Einstein condensates: Josephson effects, π oscillations and macroscopic quantum self-trapping. Phys. Rev. A, 1999, 59(1): 620-633.
[137] Williams J E. Optimal conditions for observing Josephson oscillations in a double-well Bose-Einstein condensate. Phys. Rev. A, 2001, 64(1): 013610-7.
[138] Ng H T, Law C K, Leung P T. Quantum-correlated double-well tunneling of two-component Bose-Einstein condensates. Phys. Rev. A, 2003, 68(1): 013604-6.
[139] Imamoglu A, Lewenstein M, You L. Inhibition of Coherence in Trapped Bose-Einstein Condensates. Phys. Rev. Lett., 1997, 78(13): 2511-2514.
[140] Javanainen J, Ivanov M Y. Splitting a trap containing a Bose-Einstein condensate: Atom number fluctuations. Phys. Rev. A, 1999, 60(3): 2351-2359.
[141] Peres A. Quantum Theory: Concepts and Methods. Dordrecht: Kluwer Academic, 1995.
[142] Hines A P, McKenzie R H, Milburn G J. Entanglement of two-mode Bose-Einstein condensates. Phys. Rev. A, 2003, 67(1): 013609-10.
[143] Anglin J R, Ketterle W. Bose-Einstein condensation of atomic gases . Nature, 2002, 416: 211-218.
[144] Micheli A, Jaksch D, Cirac J I et al. Many particle entanglement in two-component Bose-Einstein Condensates, cond-mat/0205369.
[145] You L. Creating Maximally Entangled Atomic States in a Bose-Einstein Condensate. Phys. Rev. Lett., 2003, 90(3): 030402-4.
[146] Leggett A J. Bose-Einstein condensation in the alkali gases: Some fundamental concepts. Rev. Mod. Phys., 2001, 73(2): 307-356.
[147] Mahmud K W, Perry H, Reinhardt W P. Quantum phase-space picture of Bose-Einstein condensates in a double well. Phys. Rev. A, 2005, 71: 023615-17.
[148] Lee H. Theory and application of the quantum phase-space distribution functions. Phys. Rep., 1995, 259(1): 147-211.
[149] Greenberger D M, Home M A, Shimony A et al. Bell's theorem without inequalities. Am. J. Phys., 1990, 58(12): 1131-1143.
[150] Bell J S. Speakable and Unspeakable in Quantum Mechanics. New York: Cambridge University Press, 1987.
[151] Chen J, Guo Y Q, Cao H J et al. Two-mode entanglement using a spin-1/2 approximation method in two-component condensates. Phys. Lett. A., 2007, 360(3): 429-434.
[152] Spekkens R W, Sipe J E. Spatial fragmentation of a Bose-Einstein condensate in a double-well potential. Phys. Rev. A, 1999, 59(5): 3868-3877.
[153] Reinhardt W P, Perry H. Fundamental World in Quantum Chemistry, edited by Brandas E J and Kryachko E S. Dordrecht: Kluwer, 2003.
[154] Myatt C J, Burt E A, Ghrist R W et al. Production of Two Overlapping Bose-Einstein Condensates by Sympathetic Cooling. Phys. Rev. Lett., 1997, 78(4): 586-589.
[155] Anglin J R, Drummond P, Smerzi A. Exact quantum phase model for mesoscopic Josephson junctions. Phys. Rev. A, 2001, 64(6): 063605-4.
[156] Bandyopadhyay A, Rai J. Uncertainties of Schwinger angular-momentum operators for squeezed radiation in interferometers. Phys. Rev. A, 1995, 51(2): 1597-1603.
[157] Hall D S, Matthews M R, Ensher J R et al. Dynamics of Component Separation in a Binary Mixture of Bose-Einstein Condensates. Phys. Rev. Lett., 1998, 81(8): 1539-1542.
[158] Law C K, Ng H T, Leung P T. Coherent control of spin squeezing. Phys. Rev. A, 2001, 63(5): 055601-3.
[159] Modugno G, Modugno M, Riboli F et al. Two Atomic Species Superfluid. Phys. Rev. Lett., 2002, 89(19): 190404-4.
[160] Chen J, Yu C S, Song H S. Elementary Quantum Gates Based on Intrinsic Interaction Hamiltonian. Commun. Theor. Phys., 2006, 46(1): 69-72.
[161] Barenco A, Bennett C H, Cleve R et al. Elementary gates for quantum computation. Phys. Rev. A, 1995, 52(5): 3457-3467.
[162] Shi Y. Both Toffoli and Controlled-NOT need little help to do universal quantum computation. quant-ph/0205115.
[163] Fredkin E, Toffoli T. Conservation logic. Internat. J. Theoret. phys., 1982, 21: 219-253.
[164] Toffoli T. Reversible Computing, in Automata, languages and Programming, eds, de Bakker J W and Van Leeuwer J. New York: Sping, 1980.
[165] Zhu S L, Wang Z D. Universal quantum gates based on a pair of orthogonal cyclic states: Application to NMR systems. Phys. Rev. A, 2003, 67(2): 022319-9.
[166] DiVincenzo D P. The Physical Implementation of Quantum Computation. Fortschr. Phys., 2000,48: 771-783.
[167] Harrow A W, Nielsen M A. Robustness of quantum gates in the presence of noise. Phys. Rev. A, 2003, 68(1): 012308-13.
[168] Cirac J I, Zoller P. Quantum Computations with Cold Trapped Ions. Phys. Rev. Lett., 1995, 74(20): 4091-4094.
[169] Pellizzari T, Gardiner S A, Cirac J I et al. Decoherence, Continuous Observation, and Quantum Computing: A Cavity QED Model. Phys. Rev. Lett., 1995, 75(21): 3788-3791.
[170] Gershenfeld N A, Chuang I L. Bulk Spin-Resonance Quantum Computation. Science, 1997, 275(5298): 350-356.
[171] Makhlin Y, Schon G, Shnirman A. Quantum-state engineering with Josephson-junction devices. Rev. Mod. Phys., 2001, 73(2): 357-400.
[172] Nakamura Y, Pashkin Y A, Tsai J S. Coherent control of macroscopic quantum states in a single- Cooper-pair box. Nature, 1999, 398: 786-788.
[173] Falci G, Fazio R, Palma G M et al. Detection of geometric phases in superconducting nanocircuits. Nature, 2000, 407: 355-358.
[174] Bacon D, Kempe J, DiVincenzo D P et al. Encoded Universality in Physical Implementations of a Quantum Computer, quant-ph/0102140.
[175] Preskill J. Lecture Notes for Physics 229: Quantum Information and Computation, California: California Institute of Technology, 1998.
[176] Mollow B R, Glauber R J. Quantum Theory of Parametric Amplification. I. Phys. Rev., 1967, 160(5): 1076-1096.
[177] Mollow B R. Quantum Statistics of Coupled Oscillator Systems. Phys. Rev., 1967, 162(5): 1256- 1273.
[178] Reid M D, Walls D F. Violations of classical inequalities in quantum optics. Phys. Rev. A, 1986, 34(2): 1260-1276.
[179] Anderson P W. Limits on the Energy of the Antiferromagnetic Ground State. Phys. Rev., 1951, 83(6): 1260-1260.
[180] Deutsch D. Universality in quantum computation. Proc. Roy. Soc. London Ser. A, 1995, 449: 669-677.
[181] Lloyd S. Almost Any Quantum Logic Gate is Universal. Phys. Rev. Lett., 1995, 75(2): 346-349.
[182] Deutsch D. Quantum computational networks. Proc. Roy. Soc. London Ser. A, 1989, 425: 73-90.
[183] Barenco A. A universal two-bit gate for quantum computation. Proc. Roy. Soc. London Ser. A, 1995, 449: 679-683. Notation: quant-ph/, cond-mat/ please see http://Arxiv.org/abs/xx-xx/xxxxxxx.