量子信息处理方案研究及其应用
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摘要
量子信息处理利用量子力学规律表示和操作信息，其能力大大超过了经典信息处理方式，因而激发了研究者对此研究领域的极大兴趣。在本论文中，我们主要讨论了两种不基于量子逻辑网络的量子信息处理方案——自由演化模型方案和一次性的量子计算机。
自由演化模型的特点很鲜明：优点是在处理过程中，无需对系统做任何含时的调控(除了某些情况下做单比特测量之外)，这样系统能够很好的独立于外界，而且对于那些实验上很难调控内部相互作用大小的系统，这种方案无疑更为容易实现；缺点是需要针对具体的任务来设计系统的具体属性，包括系统的构型，作用于其上的哈密顿量和初态等，从而影响了它的通用性。
一次性的量子计算机则是普适的，当这种量子计算机的初态即二维的cluster态制备完成之后，剩下的工作就仅仅只是一序列的单qubit测量。一次性的量子计算机没有量子输入，量子输出，量子寄存器，也不包含量子门。但是，由于利用了纠缠态作为它的核心物理资源，它的确实现了量子计算机的功能。
在第二章中，我们讨论了如何利用自由演化模型实现几项比较重要的量子信息处理任务，即量子态传输、量子态克隆、量子纠缠态制备。在量子态传输一节里介绍了如何利用具有镜像对称性的自旋网络来实现精确态传输。而在量子态克隆和量子纠缠态制备这两节里，我们利用星形自旋网络实现了最佳的1→M相位协变克隆(PCC)和W态的制备。另外，我们采用N个辅助粒子与M个目标粒子相互作用的自旋网络结构，使得需要制备的对称态在对辅助粒子进行单比特测量后能以一定的概率精确制备到目标粒子上。进一步的，我们提出“重复直到成功”的策略，即制备失败后不需要恢复系统到初始状态，继续演化并对对辅助粒子继续测量，最终能制备出所需的对称态。
鉴于图态在一次性的量子计算机中的重要性，我们在第三章中介绍了图态的一些性质，尤其是图态的测量性质和图态的等价类划分。我们还讨论了图态在量子博弈中的应用。特别地，我们详细分析了以星形结构的图态作为纠缠源的量子少数者博弈，发现当选手的数目为偶数时，选手在Nash平衡下能够得到比经典情况更多的收益。进一步的，我们研究了4qubit的图态，发现无论在哪种4
Quantum information processing employs quantum mechanics to express and manipulate information, and it appeals much more powerful than the classic information processing. Recently, this field has drawn increasing attention. In this thesis, we mainly investigate two quantum information processing schemes: free evolution model and the one-way quantum computer, both of which do not involve quantum logic network.
In the free evolution model, the time dependent external control (except for single qubit measurements) is not needed, which ensures the whole computation process can be implemented while isolated from environment. Moreover, for those systems where the interaction between qubits is difficult to modulate, this scheme provides a relative easier alternative. Meanwhile, this scheme is less flexible than the traditional approach with quantum gates. One needs to design a different system including the structure of the system, the Hamiltonian and the initial state for each different computation task.
The one-way quantum computer, in the other hand, is universal. When the initial state, a two dimensional cluster state, has been prepared, all left work is to perform a series of single qubit measurements upon chosen qubits. This scheme consists no quantum input, output and quantum register, even unitary gates from some universal sets are not necessary. However, by utilizing quantum entangled states as its kernel physical resource, it does realize all required functions of the genuine quantum computer.
In Chapter 2 we show how to implement several important quantum information
processing tasks--quantum state transfer, quantum state cloning and the generation
of quantum entangled states, within the free evolution model. We describe that perfect state transfer can be carried out in spin networks which has the mirror inversion symmetry. Later, we demonstrate that star like spin network is capable of implementing optimal 1 → M Phase Covariant Cloning (PCC), also it can also be used to generate arbitrary W states. Further, we proposed a "repeat-until-success" scheme which provides a persistent approach to arbitrary symmetric states without any modulated control.
Since the Graph state plays an crucial role in one-way quantum computer, we in-
自由演化模型的特点很鲜明：优点是在处理过程中，无需对系统做任何含时的调控(除了某些情况下做单比特测量之外)，这样系统能够很好的独立于外界，而且对于那些实验上很难调控内部相互作用大小的系统，这种方案无疑更为容易实现；缺点是需要针对具体的任务来设计系统的具体属性，包括系统的构型，作用于其上的哈密顿量和初态等，从而影响了它的通用性。
一次性的量子计算机则是普适的，当这种量子计算机的初态即二维的cluster态制备完成之后，剩下的工作就仅仅只是一序列的单qubit测量。一次性的量子计算机没有量子输入，量子输出，量子寄存器，也不包含量子门。但是，由于利用了纠缠态作为它的核心物理资源，它的确实现了量子计算机的功能。
在第二章中，我们讨论了如何利用自由演化模型实现几项比较重要的量子信息处理任务，即量子态传输、量子态克隆、量子纠缠态制备。在量子态传输一节里介绍了如何利用具有镜像对称性的自旋网络来实现精确态传输。而在量子态克隆和量子纠缠态制备这两节里，我们利用星形自旋网络实现了最佳的1→M相位协变克隆(PCC)和W态的制备。另外，我们采用N个辅助粒子与M个目标粒子相互作用的自旋网络结构，使得需要制备的对称态在对辅助粒子进行单比特测量后能以一定的概率精确制备到目标粒子上。进一步的，我们提出“重复直到成功”的策略，即制备失败后不需要恢复系统到初始状态，继续演化并对对辅助粒子继续测量，最终能制备出所需的对称态。
鉴于图态在一次性的量子计算机中的重要性，我们在第三章中介绍了图态的一些性质，尤其是图态的测量性质和图态的等价类划分。我们还讨论了图态在量子博弈中的应用。特别地，我们详细分析了以星形结构的图态作为纠缠源的量子少数者博弈，发现当选手的数目为偶数时，选手在Nash平衡下能够得到比经典情况更多的收益。进一步的，我们研究了4qubit的图态，发现无论在哪种4
Quantum information processing employs quantum mechanics to express and manipulate information, and it appeals much more powerful than the classic information processing. Recently, this field has drawn increasing attention. In this thesis, we mainly investigate two quantum information processing schemes: free evolution model and the one-way quantum computer, both of which do not involve quantum logic network.
In the free evolution model, the time dependent external control (except for single qubit measurements) is not needed, which ensures the whole computation process can be implemented while isolated from environment. Moreover, for those systems where the interaction between qubits is difficult to modulate, this scheme provides a relative easier alternative. Meanwhile, this scheme is less flexible than the traditional approach with quantum gates. One needs to design a different system including the structure of the system, the Hamiltonian and the initial state for each different computation task.
The one-way quantum computer, in the other hand, is universal. When the initial state, a two dimensional cluster state, has been prepared, all left work is to perform a series of single qubit measurements upon chosen qubits. This scheme consists no quantum input, output and quantum register, even unitary gates from some universal sets are not necessary. However, by utilizing quantum entangled states as its kernel physical resource, it does realize all required functions of the genuine quantum computer.
In Chapter 2 we show how to implement several important quantum information
processing tasks--quantum state transfer, quantum state cloning and the generation
of quantum entangled states, within the free evolution model. We describe that perfect state transfer can be carried out in spin networks which has the mirror inversion symmetry. Later, we demonstrate that star like spin network is capable of implementing optimal 1 → M Phase Covariant Cloning (PCC), also it can also be used to generate arbitrary W states. Further, we proposed a "repeat-until-success" scheme which provides a persistent approach to arbitrary symmetric states without any modulated control.
Since the Graph state plays an crucial role in one-way quantum computer, we in-
引文
[1] R. Landauer. Irreversibility and heat generation in the computing process[J]. IBM J Res Develop. 1961, 5(3): 183-191
[2] A. Steane. Quantum computing[J]. Rep Prog Phys, 1998, 61:117-173
[3] C. H. Bennett, D. P. Divincenzo. Quantum information and computation[J]. Nature (London). 2000, 404(6775):247-255
[4] C. H. Bennett. Quantum information and computation[J]. Physics Today. 1995, 48(10):24-30
[5] M. A. Nielsen. Introduction to quantum information theory[J]. ArXiv Quantum Physics e-prints. Nov. 2000. arXiv:quant-ph/0011064
[6] J. Preskill. Quantum information and physics: some future directions[J]. 2000
[7] J. Preskill. A course for quantum information and computation[M]. 1997
[8] A. Ekert, P. Hayden. Basic concepts in quantum computation[J]. ArXiv Quantum Physics e-prints. Nov. 2000. arXiv:quant-ph/0011013
[9] D. Bouwmeester, A. Ekert, A. Zeilinger. The physics of quantum information[M]. Springer-Verlag, 2000
[10] Nielsen M. A., Chuang I. L. Quantum computation and information[M]. Cambridge, Cambridge University Press, 2000
[11] P. Busch, M. Grabowski, P. J. Lahti. Operational quantum physics[M]. Beijing, World Publishing Corporation, First Edition, 1999
[12] R. P. Feynman. Simulating physics with computers[J]. Int J Theor Phys. 1982, 21(6-7):467-488
[13] 郭光灿．量子信息引论[J]．量子力学新进展(第一缉)．2000，1(1)：249-285
[14] 郭光灿．量子信息引论[J]．物理．2001，30(5)：286-293
[15] R. Raussendorf. Measurement-based quantum computation with cluster states[D], 博士学位论文， Ludwig-Maximilians-Universitat, LMU, Miinchen, Germany, 2003
[16] W. K. Wootters, W. H. Zurek. A single quantum cannot be cloned[J]. Nature. 1982, 299:802-803
[17] C. H. Bennett. Logical reversibility of computation[J]. IBM J Res Develop. 1973, 17(6):525-532
[18] P. Benioff. The Computer as a Physical System: A Microscopic Quantum Mechanical Hamiltonian Model of Computers as Represented by Turing Machines[J]. J Stat Phys. 1980, 22(5):563-591
[19] P. Benioff. Quantum mechanical Hamiltonian models of Turing machines[J]. J Stat Phys. 1982,29:515
[20] D. Deutsch. Quantum theory, the Church-Turing principle and the universal quantum com- puter[J]. Proc R Soc Lond A. 1985, 400(1818):97-117
[21] D. Deutsch. Quantum computational networks[J]. Proc Roy Soc Lond A. 1989, 425(1868):73-90
[22] A. Barenco, et al. Elementary gates for quantum computation[J]. Phys Rev A. 1995, 52(5):3457-3467
[23] P. O. Boykin, et al. A universal and fault-tolerant quantum basis[J]. Inf Proc Lett. 2000, 75:101
[24] Nielsen M. A., Chuang I. L. Quantum computation and information[M]. Cambridge, Cam- bridge University Press, 2000
[25] S. C. Benjamin. Simple pulses for universal quantum computation with a Heisenberg ABA B chain[J]. Phys Rev A. 2001, 64(5):054303
[26] D. P. Divincenzo, D. Bacon, J. Kempe, G. Burkard, K. B. Whaley. Universal quantum computation with the exchange interaction[J]. Nature. 2000, 408(6810):339 - 342
[27] B. E. Kane. A silicon-based nuclear spin quantum computer[J]. Nature. 1998, 393(6681):133-137
[28] D. Loss, D. P. Divincenzo. Quantum computation with quantum dots[J]. Phys Rev A. 1998, 57(1):120- 126
[29] R. Vrijen, E. Yablonovitch, K. Wang, H. W. Jiang, A. Balandin, V. Roychowdhury, T. Mor, D. Divincenzo. Electron-spin-resonance transistors for quantum computing in silicon- germanium heterostructures[J]. Phys Rev A. 2000, 62(1):art. no. - 012306
[30] S. C. Benjamin, S. Bose. Quantum computing with an always-on Heisenberg interaction[J]. Phys Rev Lett. 2003, 90(24):247901
[31] S. Bose. Quantum communication through an unmodulated spin chain [J]. Phys Rev Lett. 2003, 91(20):207901
[32] G. De chiara, R. Fazio, C. Macchiavello, S. Montangero, G. M. Palma. Cloning transforma- tions in spin networks without external control[J]. Phys Rev A. 2005, 72(1):012328
[33] L. W. Beineke, R. J Wilson. Selected Topics in Graph Theory[M]. London, Academic Press, 1978
[34] HARARY F., PALMER E. M. Graphical Enumeration[M]. NY, Academic Press, 1973
[35] C. H. Bennett, D. P. Divincenzo. Quantum information and computation[J]. Nature. 2000, 404(6775):247 - 255
[36] D. Kielpinski, C. Monroe, D. J. Wineland. Architecture for a large-scale ion-trap quantum computer[J]. Nature. 2002, 417(6890):709-711
[37] C. Albanese, M. Christandl, N. Datta, A. Ekert. Mirror inversion of quantum states in linear registers[J]. Phys Rev Lett. 2004, 93(23):230502
[38] M. Christandl, N. Datta, A. Ekert, A. J. Landahl. Perfect state transfer in quantum spin networks[J]. Phys Rev Lett. 2004, 92(18): 187902
[39] M. Christandl, N. Datta, T. C. Dorlas, A. Ekert, A. Kay, A. J. Landahl. Perfect transfer of arbitrary states in quantum spin networks[J]. Phys Rev A. 2005, 71(3):032312
[40] D. Burgarth, V. Giovannetti, S. Bose. Efficient and perfect state transfer in quantum chains[J]. J Phys A: Math Gen. 2005, 38(30):6793 - 6802
[41 ] D. Burgarth, S. Bose. Conclusive and arbitrarily perfect quantum-state transfer using parallel spin-chain channels[J]. Phys Rev A. 2005,71(5):052315
[42] D. Burgarth, S. Bose. Perfect quantum state transfer with randomly coupled quantum chains[J]. New J Phys. 2005,7:135
[43] B. Vaucher, D. Burgarth, S. Bose. Arbitrarily perfect quantum communication using unmodulated spin chains, a collaborative approach[J]. JOURNAL OF OPTICS B-QUANTUM AND SEMICLASSICAL OPTICS. 2005, 7(10):S356 - S362
[44] V. Giovannetti, D. Burgarth. Improved transfer of quantum information using a local mem-ory[J]. Phys Rev Lett. 2006, 96(3):030501
[45] A. Kay. Perfect state transfer: Beyond nearest-neighbor couplings[J]. Phys Rev A. 2006, 73(3):032306
[46] A. Lyakhov, C. Bruder. Quantum state transfer in arrays of flux qubits[J]. New J Phys. 2005, 7:181
[47] M. Paternostro, G. M. Palma, M. S. Kim, G. Falci. Quantum-state transfer in imperfect artificial spin networks[J]. Phys Rev A. 2005,71(4):042311
[48] X. F. Qian, Y. Li, Y. Li, Z. Song, C. P. Sun. Quantum-state transfer characterized by mode entanglement[J]. Phys Rev A. 2005, 72(6):062329
[49] Z. Song, C. P. Sun. Quantum information storage and state transfer based on spin systems[J]. Low Temp Phys. 2005, 31(8-9):686 - 694
[50] T. Shi, Y. Li, Z. Song, C. P. Sun. Quantum-state transfer via the ferromagnetic chain in a spatially modulated field[J]. Phys Rev A. 2005, 71(3):032309
[51] A. Wojcik, T. Luczak, P. Kurzynski, A. Grudka, T. GdaIa, M. Bednarska. Unmodulated spin chains as universal quantum wires[J]. Phys Rev A. 2005, 72(3):034303
[69] A. Lamas-Linares, C. Simon, J. C. Howell, D. Bouwmeester. Experimental quantum cloning of single photons[J]. Science. 2002, 296(5568):712-714
[70] D. Pelliccia, V. Schettini, F. Sciarrino, C. Sias, F. De martini. Contextual realization of the universal quantum cloning machine and of the universal-NOT gate by quantum-injected optical parametric amplification[J]. Phys Rev A. 2003, 68(4):042306
[71] F. De martini, D. Pelliccia, F. Sciarrino. Contextual, optimal, and universal realization of the quantum cloning machine and of the NOT gate[J]. Phys Rev Lett. 2004, 92(6):067901
[72] J. F. Du, T. Durt, P. Zou, H. Li, L. C. Kwek, C. H. Lai, C. H. Oh, A. Ekert. Experimental quantum cloning with prior partial information[J]. Phys Rev Lett. 2005, 94(4):040505
[73] G. De chiara, R. Fazio, C. Macchiavello, S. Montangero, G. M. Palma. Quantum cloning in spin networks[J]. Phys Rev A. 2004, 70(6):062308
[74] Q. Chen, J. Cheng, K.-L. Wang, J. Du. Optimal quantum cloning via spin networks[J]. ArXiv Quantum Physics e-prints. Oct. 2005. arXiv:quant-ph/0510147
[75] A. Hutton, S. Bose. Mediated entanglement and correlations in a star network of interacting spins[J]. Phys Rev A. 2004, 69(4):042312
[76] R. H. Dicke. Coherence in spontaneous radiation processes [J]. Phys Rev. 1954, 93(1):99-110
[77] S. F. Huelga, C. Macchiavello, T. Pellizzari, A. K. Ekert, M. B. Plenio, J. I. Cirac. Improvement of frequency standards with quantum entanglement[J]. Phys Rev Lett. 1997, 79(20):3865 - 3868
[78] J. Vidal. Concurrence in collective models[J]. ArXiv Quantum Physics e-prints. Mar. 2006. arXi v:qaant-ph/0603108
[79] C. N. Yang. (?) pairing and off-diagonal long-range order in a Hubbard model[J]. Phys Rev Lett. 1989, 63:2144
[80] V. Vedral. High-temperature macroscopic entanglement[J]. New J Phys. 2004,6:102
[81] P. Kaye, M. Mosca. Quantum Networks for Generating Arbitrary Quantum States[J]. ArXiv Quantum Physics e-prints. Jul. 2004. arXiv:quant-ph/0407102
[82] R. G. Unanyan, M. Fleischhauer, N. V. Vitanov, K. Bergmann. Entanglement generation by adiabatic navigation in the space of symmetric multiparticle states[J]. Phys Rev A. 2002, 66(4):042101
[83] S. Hill, W. K. Wootters. Entanglement of a pair of quantum bits[J]. Phys Rev Lett. 1997, 78(26):5022 - 5025
[84] W. K. Wootters. Entanglement of formation of an arbitrary state of two qubits[J]. Phys Rev Lett. 1998, 80(10):2245-2248
[85] X. Wang, K. Molmer. Pairwise entanglement in symmetric multi-qubit systems[J]. Eur Phys JD. 2002,18(3):385- 391
[86] K. M. O'connor, W. K. Wootters. Entangled rings[J]. Phys Rev A. 2001, 63(5):052302
[87] T. C. Wei, P. M. Goldbart. Geometric measure of entanglement and applications to bipartite and multipartite quantum states[J]. Phys Rev A. 2003, 68(4):042307
[88] Q. Chen, J. Cheng, K.-L. Wang, J. Du. Repeat-Until-Success Generation of Symmetric States without External Control[J]. ArXiv Quantum Physics e-prints. Apr. 2006. arXiv:quant-ph/0604204
[89] A. Olaya-Castro, N. F. Johnson, L. Quiroga. Robust one-step catalytic machine for high fidelity anticloning and W-state generation in a multiqubit system[J]. Phys Rev Lett. 2005, 94(11): 110502
[90] H. J. Briegel, R. Raussendorf. Persistent entanglement in arrays of interacting particles[J]. Phys Rev Lett. 2001, 86(5):910 - 913
[91] R. Raussendorf, H. J. Briegel. A one-way quantum computer[J]. Phys Rev Lett. 2001, 86(22):5188-5191
[92] M. Hein, W. Diir, J. Eisert, R. Raussendorf, M. Van den Nest, H. . Briegel. Entanglement in Graph States and its Applications[J]. ArXiv Quantum Physics e-prints. Feb. 2006. arXiv:quant-ph/0602096
[93] A. Bouchet. An efficient algorithm to recognize locally equivalent graphs[J]. Combinatorica. 1991,11(4):315-329
[94] A. Bouchet. Recognizing locally equivalent graphs[J]. Discrete Mmathematics. 1993,114(1-3): 75 - 86
[95] Glynn D. G. On self-dual quantum codes and graphs[J]. Submitted to Electronic Journal of Combinatorics, Preprint. 2002
[96] Dehaene J. Van Den Nest M., De Moor B. Graphical description of the action of local Clifford transformations on graph states[J]. Phys Rev A. 2004, 69:022316
[97] M. Hein, J. Eisert, H. J. Briegel. Multiparty entanglement in graph states[J]. Phys Rev A. 2004,69(6):062311
[98] D. Schlingemann. Cluster states, algorithms and graphs[J]. Quant Inf Comp. 2004,4(4):289 -324
[99] D. Fon-Der-Flaass. Local equivalence of transversals in matroids[J]. Electr J Comb. 1996, 3(1)
[100] M. Van den nest, J. Dehaene, B. De moor. Local unitary versus local Clifford equivalence of stabilizer states[J]. Phys Rev A. 2005, 71(6):062323
[101] M. Van den nest, J. Dehaene, B. De moor. Local invariants of stabilizer codes[J]. Phys Rev A. 2004, 70(3):032323
[102] M. Van den nest, J. Dehaene, B. De moor. Invariants of the local Clifford group[J]. Phys Rev A. 2005, 71(2): 022310
[103] J. Eisert, H. J. Briegel. Schmidt measure as a tool for quantifying multiparticle entanglement[J]. Phys Rev A. 2001, 64(2): 022306
[104] M. Hein. Entanglement in Graph States[D]. 博士学位论文， University of Innsbruck, Austria, 2005
[105] O. Guhne, G. Toth, P. Hyllus, H. J. Briegel. Bell inequalities for graph states[J]. Phys Rev Lett. 2005, 95(12): 120405
[106] G. Toth, O. Guhne. Detecting genuine multipartite entanglement with two local measurements[J]. Phys Rev Lett. 2005, 94(6):060501
[107] G. Toth, O. Guhne, H. J. Briegel. Two-setting Bell inequalities for graph states[J]. Phys Rev A. 2006, 73(2):022303
[108] 张维迎．《博弈论与信息经济学》[M]．上海人民出版社，1996
[109] 施锡铨．《博弈论》[M]．上海财经大学出版社，2000
[110] M. A. Nowak, K. Sigmund.[J]. Nature. 1999, 398: 367
[111] J. Von Neumann, O. Morgenstern. Theory of Games and Economic Behavior[M]. Princeton University Press, Second Ed., 1947
[112] Richard Cleve, Harry Buhrman. Substituting quantum entanglement for communication[J]. Phys Rev A (Atomic, Molecular, and Optical Physics). 1997, 56(2): 1201-1204
[113] Artur K. Ekert. Quantum cryptography based on Bell's theorem[J]. Phys Rev Lett. 1991, 67(6): 661-663
[114] David A. Meyer. Quantum Strategies[J]. Phys Rev Lett. 1999, 82(5): 1052-1055
[115] D. A. Meyer. Quantum Games and Quantum Algorithms[J]. quant-ph/0004092, to appear in the AMS Contemporary Mathematics volume: Quantum Computation and Quantum Information Science. 2000
[116] Jens Eisert, Martin Wilkens, Maciej Lewenstein. Quantum Games and Quantum Strategies[J]. Phys Rev Lett. 1999, 83(15): 3077-3080
[117] Simon C. Benjamin, Patrick M. Hayden. Multiplayer quantum games[J]. Phys Rev A (Atomic, Molecular, and Optical Physics). 2001, 64(3): 030301 (pages 4)
[118] Jiangfeng Du, Hui Li, Xiaodong Xu, Xianyi Zhou, Rongdian Han. Entanglement enhanced multiplayer quantum games[J]. Phys Lett A. 2002/9/30, 302(5-6):229-233
[119] Jiangfeng Du, Xiaodong Xu, Hui Li, Xianyi Zhou, Rongdian Han. Entanglement playing a dominating role in quantum games[J]. Phys Lett A. 2001/10/8, 289(1-2): 9-15
[120] Jiangfeng Du, Hui Li, Xiaodong Xu, Mingjun Shi, Jihui Wu, Xianyi Zhou, Rongdian Han. Experimental Realization of Quantum Games on a Quantum Computer[J]. Phys Rev Lett. 2002, 88(13): 137902 (pages 4)
[121] 杜江峰，李卉，许晓栋．《量子力学新进展》(第三辑)第五章《量子博弈论》[M]．清华大学出版社 曾谨言 龙桂鲁 裴寿镛主编，2003年10月
[122] W. B. Arthur.[J]. Am Econ Assoc Papers and Proc. 1994, 84: 406
[123] Q. Chen, W. Yi, J. T. Liu, K. L. Wang. N-player quantum minority game[J]. Phys Lett A. 2004, 327(2-3): 98-102
[124] R. Raussendorf, D. E. Browne, H. J. Briegel. The one-way quantum computer-a nonnetwork model of quantum computation[J]. J Mod Optics. 2002, 49(8): 1299-1306
[125] R. Raussendorf, D. E. Browne, H. J. Briegel. Measurement-based quantum computation on cluster states[J]. Phys Rev A. 2003, 68(2):022312
[126] M. A. Nielsen. Cluster-state quantum computation[J]. Rep Math Phys. 2006, 57(1):147-161
[127] S. R. Clark, C. M. Alves, D. Jaksch. Efficient generation of graph states for quantum computation[J]. New J Phys. 2005, 7: 124
[128] M. Borhani, D. Loss. Cluster states from Heisenberg interactions[J]. Phys Rev A. 2005, 71(3): 034308
[129] M. Mhalla, S. Perdrix. Complexity of Graph State Preparation[J]. ArXiv Quantum Physics e-prints. Dec. 2004. arXiv: quant-ph/0412071
[130] Raussendorf R. Briegel H. J., Schenzle A. Optical lattices as a playground for studying multiparticle entanglement[M]. Springer, 2002
[131] D. Jaksch, H. J. Briegel, J. I. Cirac, C. W. Gardiner, P. Zoller. Entanglement of atoms via cold controlled collisions[J]. Phys Rev Lett. 1999, 82(9): 1975-1978
[132] H. J. Briegel, T. Calarco, D. Jaksch, J. I. Cirac, P. Zoller. Quantum computing with neutral atoms[J]. J Mod Optics. 2000, 47(2-3): 415-451
[133] L. M. Duan, E. Demler, M. D. Lukin. Controlling spin exchange interactions of ultracold atoms in optical lattices[J]. Phys Rev Lett. 2003, 91(9): 090402
[134] D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, P. Zoller. Cold bosonic atoms in optical lattices[J]. Phys Rev Lett. 1998, 81(15): 3108-3111
[135] M. Greiner, O. Mandel, T. W. Hansch, I. Bloch. Collapse and revival of the matter wave field of a Bose-Einstein condensate[J]. Nature. 2002, 419(6902):51-54
[136] M. Greiner, O. Mandel, T. Esslinger, T. W. Hansch, I. Bloch. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms[J]. Nature. 2002, 415(6867): 39-44
[137] O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hansch, I. Bioch. Controlled collisions for multi-particle entanglement of optically trapped atoms[J]. Nature. 2003, 425(6961):937 -940
[138] P. Rabl, A. J. Daley, P. O. Fedichev, J. I. Cirac, P. Zoller. Defect-suppressed atomic crystals in an optical lattice[J]. Phys Rev Lett. 2003,91(11):110403
[139] K. G. H. Vollbrecht, E. Solano, J. I. Cirac. Ensemble quantum computation with atoms in periodic potentials[J]. Phys Rev Lett. 2004, 93(22):220502
[140] E. Knill, R. Laflamme, G. J. Milburn. A scheme for efficient quantum computation with linear optics[J]. Nature. 2001, 409(6816):46- 52
[141] N. Yoran, B. Reznik. Deterministic linear optics quantum computation with single photon qubits[J]. Phys Rev Lett. 2003, 91(3):037903
[142] M. A. Nielsen. Optical quantum computation using cluster states[J]. Phys Rev Lett. 2004, 93(4):040503
[143] D. E. Browne, T. Rudolph. Resource-efficient linear optical quantum computation[J]. Phys Rev Lett. 2005, 95(1):010501
[144] T. C. Ralph, A. J. F. Hayes, A. Gilchrist. Loss-tolerant optical qubits[J]. Phys Rev Lett. 2005, 95(10): 100501
[145] A. N. Zhang, C. Y. Lu, X. Q. Zhou, Y. A. Chen, Z. Zhao, T. Yang, J. W. Pan. Experimental construction of optical multiqubit cluster states from Bell states[J]. Phys Rev A. 2006, 73(2):022330
[146] P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, A. Zeilinger. Experimental one-way quantum computing[J]. Nature. 2005, 434(7030): 169 - 176
[147] S. D. Barrett, P. Kok. Efficient high-fidelity quantum computation using matter qubits and linear optics[J]. Phys Rev A. 2005, 71(6):060310
[148] S. C. Benjamin, J. Eisert, T. M. Stace. Optical generation of matter qubit graph states[J]. New J Phys. 2005,7:194
[149] Y. L. Lim, A. Beige, L. C. Kwek. Repeat-until-success linear optics distributed quantum computing[J]. Phys Rev Lett. 2005, 95(3):030505
[150] Y. L. Lim, S. D. Barrett, A. Beige, P. Kok, L. C. Kwek. Repeat-until-success quantum computing using stationary and flying qubits[J]. Phys Rev A. 2006, 73(1):012304
[151] X. L. Zhang, M. Feng, K. L. Gao. Cluster-state preparation and multipartite entanglement analyzer with fermions[J]. Phys Rev A. 2006, 73(1):014301
[152] L. M. Duan, R. Raussendorf. Efficient quantum computation with probabilistic quantum gates[J]. Phys Rev Lett. 2005, 95(8):080503
[153] Q. Chen, J. H. Cheng, K. L. Wang, J. F. Du. Efficient construction of two-dimensional cluster states with probabilistic quantum gates[J]. Phys Rev A. 2006. arXiv:quant-ph/0507066
[154] M. Hein, W. Dur, H. J. Briegel. Entanglement properties of multipartite entangled states under the influence of decoherence[J]. Phys Rev A. 2005, 71(3):032350
[155] HJ Briegel, BG Englert. Quantum optical mater-quations - the use of damping bases[J]. Phys Rev A. 1993, 47(4):3311 - 3329
[156] W Dur, JI Cirac. Activating bound entanglement in multiparticle systems[J]. Phys Rev A. 2000, 62(2):022302
[157] W Dur, JI Cirac. Classification of multiqubit mixed states: Separability and distillability properties[J]. Phys Rev A. 2000, 61(4):042314
[158] W Dur, JI Cirac. Multiparticle entanglement and its experimental detection[J]. J Phys A: Math Gen. 2001, 34(35):6837 - 6850
[159] M Horodecki, P Horodecki, R Horodecki. Inseparable two spin-1/2 density matrices can be distilled to a singlet form[J]. Phys Rev Lett. 1997,78(4):574 - 577
[160] A Peres. Separability criterion for density matrices[J]. Phys Rev Lett. 1996, 77(8): 1413 -1415
[161] M Horodecki, P Horodecki, R Horodecki. Separability of mixed states: Necessary and sufficient conditions[J]. Phys Lett A. 1996, 223(1-2):1 - 8
[2] A. Steane. Quantum computing[J]. Rep Prog Phys, 1998, 61:117-173
[3] C. H. Bennett, D. P. Divincenzo. Quantum information and computation[J]. Nature (London). 2000, 404(6775):247-255
[4] C. H. Bennett. Quantum information and computation[J]. Physics Today. 1995, 48(10):24-30
[5] M. A. Nielsen. Introduction to quantum information theory[J]. ArXiv Quantum Physics e-prints. Nov. 2000. arXiv:quant-ph/0011064
[6] J. Preskill. Quantum information and physics: some future directions[J]. 2000
[7] J. Preskill. A course for quantum information and computation[M]. 1997
[8] A. Ekert, P. Hayden. Basic concepts in quantum computation[J]. ArXiv Quantum Physics e-prints. Nov. 2000. arXiv:quant-ph/0011013
[9] D. Bouwmeester, A. Ekert, A. Zeilinger. The physics of quantum information[M]. Springer-Verlag, 2000
[10] Nielsen M. A., Chuang I. L. Quantum computation and information[M]. Cambridge, Cambridge University Press, 2000
[11] P. Busch, M. Grabowski, P. J. Lahti. Operational quantum physics[M]. Beijing, World Publishing Corporation, First Edition, 1999
[12] R. P. Feynman. Simulating physics with computers[J]. Int J Theor Phys. 1982, 21(6-7):467-488
[13] 郭光灿．量子信息引论[J]．量子力学新进展(第一缉)．2000，1(1)：249-285
[14] 郭光灿．量子信息引论[J]．物理．2001，30(5)：286-293
[15] R. Raussendorf. Measurement-based quantum computation with cluster states[D], 博士学位论文， Ludwig-Maximilians-Universitat, LMU, Miinchen, Germany, 2003
[16] W. K. Wootters, W. H. Zurek. A single quantum cannot be cloned[J]. Nature. 1982, 299:802-803
[17] C. H. Bennett. Logical reversibility of computation[J]. IBM J Res Develop. 1973, 17(6):525-532
[18] P. Benioff. The Computer as a Physical System: A Microscopic Quantum Mechanical Hamiltonian Model of Computers as Represented by Turing Machines[J]. J Stat Phys. 1980, 22(5):563-591
[19] P. Benioff. Quantum mechanical Hamiltonian models of Turing machines[J]. J Stat Phys. 1982,29:515
[20] D. Deutsch. Quantum theory, the Church-Turing principle and the universal quantum com- puter[J]. Proc R Soc Lond A. 1985, 400(1818):97-117
[21] D. Deutsch. Quantum computational networks[J]. Proc Roy Soc Lond A. 1989, 425(1868):73-90
[22] A. Barenco, et al. Elementary gates for quantum computation[J]. Phys Rev A. 1995, 52(5):3457-3467
[23] P. O. Boykin, et al. A universal and fault-tolerant quantum basis[J]. Inf Proc Lett. 2000, 75:101
[24] Nielsen M. A., Chuang I. L. Quantum computation and information[M]. Cambridge, Cam- bridge University Press, 2000
[25] S. C. Benjamin. Simple pulses for universal quantum computation with a Heisenberg ABA B chain[J]. Phys Rev A. 2001, 64(5):054303
[26] D. P. Divincenzo, D. Bacon, J. Kempe, G. Burkard, K. B. Whaley. Universal quantum computation with the exchange interaction[J]. Nature. 2000, 408(6810):339 - 342
[27] B. E. Kane. A silicon-based nuclear spin quantum computer[J]. Nature. 1998, 393(6681):133-137
[28] D. Loss, D. P. Divincenzo. Quantum computation with quantum dots[J]. Phys Rev A. 1998, 57(1):120- 126
[29] R. Vrijen, E. Yablonovitch, K. Wang, H. W. Jiang, A. Balandin, V. Roychowdhury, T. Mor, D. Divincenzo. Electron-spin-resonance transistors for quantum computing in silicon- germanium heterostructures[J]. Phys Rev A. 2000, 62(1):art. no. - 012306
[30] S. C. Benjamin, S. Bose. Quantum computing with an always-on Heisenberg interaction[J]. Phys Rev Lett. 2003, 90(24):247901
[31] S. Bose. Quantum communication through an unmodulated spin chain [J]. Phys Rev Lett. 2003, 91(20):207901
[32] G. De chiara, R. Fazio, C. Macchiavello, S. Montangero, G. M. Palma. Cloning transforma- tions in spin networks without external control[J]. Phys Rev A. 2005, 72(1):012328
[33] L. W. Beineke, R. J Wilson. Selected Topics in Graph Theory[M]. London, Academic Press, 1978
[34] HARARY F., PALMER E. M. Graphical Enumeration[M]. NY, Academic Press, 1973
[35] C. H. Bennett, D. P. Divincenzo. Quantum information and computation[J]. Nature. 2000, 404(6775):247 - 255
[36] D. Kielpinski, C. Monroe, D. J. Wineland. Architecture for a large-scale ion-trap quantum computer[J]. Nature. 2002, 417(6890):709-711
[37] C. Albanese, M. Christandl, N. Datta, A. Ekert. Mirror inversion of quantum states in linear registers[J]. Phys Rev Lett. 2004, 93(23):230502
[38] M. Christandl, N. Datta, A. Ekert, A. J. Landahl. Perfect state transfer in quantum spin networks[J]. Phys Rev Lett. 2004, 92(18): 187902
[39] M. Christandl, N. Datta, T. C. Dorlas, A. Ekert, A. Kay, A. J. Landahl. Perfect transfer of arbitrary states in quantum spin networks[J]. Phys Rev A. 2005, 71(3):032312
[40] D. Burgarth, V. Giovannetti, S. Bose. Efficient and perfect state transfer in quantum chains[J]. J Phys A: Math Gen. 2005, 38(30):6793 - 6802
[41 ] D. Burgarth, S. Bose. Conclusive and arbitrarily perfect quantum-state transfer using parallel spin-chain channels[J]. Phys Rev A. 2005,71(5):052315
[42] D. Burgarth, S. Bose. Perfect quantum state transfer with randomly coupled quantum chains[J]. New J Phys. 2005,7:135
[43] B. Vaucher, D. Burgarth, S. Bose. Arbitrarily perfect quantum communication using unmodulated spin chains, a collaborative approach[J]. JOURNAL OF OPTICS B-QUANTUM AND SEMICLASSICAL OPTICS. 2005, 7(10):S356 - S362
[44] V. Giovannetti, D. Burgarth. Improved transfer of quantum information using a local mem-ory[J]. Phys Rev Lett. 2006, 96(3):030501
[45] A. Kay. Perfect state transfer: Beyond nearest-neighbor couplings[J]. Phys Rev A. 2006, 73(3):032306
[46] A. Lyakhov, C. Bruder. Quantum state transfer in arrays of flux qubits[J]. New J Phys. 2005, 7:181
[47] M. Paternostro, G. M. Palma, M. S. Kim, G. Falci. Quantum-state transfer in imperfect artificial spin networks[J]. Phys Rev A. 2005,71(4):042311
[48] X. F. Qian, Y. Li, Y. Li, Z. Song, C. P. Sun. Quantum-state transfer characterized by mode entanglement[J]. Phys Rev A. 2005, 72(6):062329
[49] Z. Song, C. P. Sun. Quantum information storage and state transfer based on spin systems[J]. Low Temp Phys. 2005, 31(8-9):686 - 694
[50] T. Shi, Y. Li, Z. Song, C. P. Sun. Quantum-state transfer via the ferromagnetic chain in a spatially modulated field[J]. Phys Rev A. 2005, 71(3):032309
[51] A. Wojcik, T. Luczak, P. Kurzynski, A. Grudka, T. GdaIa, M. Bednarska. Unmodulated spin chains as universal quantum wires[J]. Phys Rev A. 2005, 72(3):034303
[69] A. Lamas-Linares, C. Simon, J. C. Howell, D. Bouwmeester. Experimental quantum cloning of single photons[J]. Science. 2002, 296(5568):712-714
[70] D. Pelliccia, V. Schettini, F. Sciarrino, C. Sias, F. De martini. Contextual realization of the universal quantum cloning machine and of the universal-NOT gate by quantum-injected optical parametric amplification[J]. Phys Rev A. 2003, 68(4):042306
[71] F. De martini, D. Pelliccia, F. Sciarrino. Contextual, optimal, and universal realization of the quantum cloning machine and of the NOT gate[J]. Phys Rev Lett. 2004, 92(6):067901
[72] J. F. Du, T. Durt, P. Zou, H. Li, L. C. Kwek, C. H. Lai, C. H. Oh, A. Ekert. Experimental quantum cloning with prior partial information[J]. Phys Rev Lett. 2005, 94(4):040505
[73] G. De chiara, R. Fazio, C. Macchiavello, S. Montangero, G. M. Palma. Quantum cloning in spin networks[J]. Phys Rev A. 2004, 70(6):062308
[74] Q. Chen, J. Cheng, K.-L. Wang, J. Du. Optimal quantum cloning via spin networks[J]. ArXiv Quantum Physics e-prints. Oct. 2005. arXiv:quant-ph/0510147
[75] A. Hutton, S. Bose. Mediated entanglement and correlations in a star network of interacting spins[J]. Phys Rev A. 2004, 69(4):042312
[76] R. H. Dicke. Coherence in spontaneous radiation processes [J]. Phys Rev. 1954, 93(1):99-110
[77] S. F. Huelga, C. Macchiavello, T. Pellizzari, A. K. Ekert, M. B. Plenio, J. I. Cirac. Improvement of frequency standards with quantum entanglement[J]. Phys Rev Lett. 1997, 79(20):3865 - 3868
[78] J. Vidal. Concurrence in collective models[J]. ArXiv Quantum Physics e-prints. Mar. 2006. arXi v:qaant-ph/0603108
[79] C. N. Yang. (?) pairing and off-diagonal long-range order in a Hubbard model[J]. Phys Rev Lett. 1989, 63:2144
[80] V. Vedral. High-temperature macroscopic entanglement[J]. New J Phys. 2004,6:102
[81] P. Kaye, M. Mosca. Quantum Networks for Generating Arbitrary Quantum States[J]. ArXiv Quantum Physics e-prints. Jul. 2004. arXiv:quant-ph/0407102
[82] R. G. Unanyan, M. Fleischhauer, N. V. Vitanov, K. Bergmann. Entanglement generation by adiabatic navigation in the space of symmetric multiparticle states[J]. Phys Rev A. 2002, 66(4):042101
[83] S. Hill, W. K. Wootters. Entanglement of a pair of quantum bits[J]. Phys Rev Lett. 1997, 78(26):5022 - 5025
[84] W. K. Wootters. Entanglement of formation of an arbitrary state of two qubits[J]. Phys Rev Lett. 1998, 80(10):2245-2248
[85] X. Wang, K. Molmer. Pairwise entanglement in symmetric multi-qubit systems[J]. Eur Phys JD. 2002,18(3):385- 391
[86] K. M. O'connor, W. K. Wootters. Entangled rings[J]. Phys Rev A. 2001, 63(5):052302
[87] T. C. Wei, P. M. Goldbart. Geometric measure of entanglement and applications to bipartite and multipartite quantum states[J]. Phys Rev A. 2003, 68(4):042307
[88] Q. Chen, J. Cheng, K.-L. Wang, J. Du. Repeat-Until-Success Generation of Symmetric States without External Control[J]. ArXiv Quantum Physics e-prints. Apr. 2006. arXiv:quant-ph/0604204
[89] A. Olaya-Castro, N. F. Johnson, L. Quiroga. Robust one-step catalytic machine for high fidelity anticloning and W-state generation in a multiqubit system[J]. Phys Rev Lett. 2005, 94(11): 110502
[90] H. J. Briegel, R. Raussendorf. Persistent entanglement in arrays of interacting particles[J]. Phys Rev Lett. 2001, 86(5):910 - 913
[91] R. Raussendorf, H. J. Briegel. A one-way quantum computer[J]. Phys Rev Lett. 2001, 86(22):5188-5191
[92] M. Hein, W. Diir, J. Eisert, R. Raussendorf, M. Van den Nest, H. . Briegel. Entanglement in Graph States and its Applications[J]. ArXiv Quantum Physics e-prints. Feb. 2006. arXiv:quant-ph/0602096
[93] A. Bouchet. An efficient algorithm to recognize locally equivalent graphs[J]. Combinatorica. 1991,11(4):315-329
[94] A. Bouchet. Recognizing locally equivalent graphs[J]. Discrete Mmathematics. 1993,114(1-3): 75 - 86
[95] Glynn D. G. On self-dual quantum codes and graphs[J]. Submitted to Electronic Journal of Combinatorics, Preprint. 2002
[96] Dehaene J. Van Den Nest M., De Moor B. Graphical description of the action of local Clifford transformations on graph states[J]. Phys Rev A. 2004, 69:022316
[97] M. Hein, J. Eisert, H. J. Briegel. Multiparty entanglement in graph states[J]. Phys Rev A. 2004,69(6):062311
[98] D. Schlingemann. Cluster states, algorithms and graphs[J]. Quant Inf Comp. 2004,4(4):289 -324
[99] D. Fon-Der-Flaass. Local equivalence of transversals in matroids[J]. Electr J Comb. 1996, 3(1)
[100] M. Van den nest, J. Dehaene, B. De moor. Local unitary versus local Clifford equivalence of stabilizer states[J]. Phys Rev A. 2005, 71(6):062323
[101] M. Van den nest, J. Dehaene, B. De moor. Local invariants of stabilizer codes[J]. Phys Rev A. 2004, 70(3):032323
[102] M. Van den nest, J. Dehaene, B. De moor. Invariants of the local Clifford group[J]. Phys Rev A. 2005, 71(2): 022310
[103] J. Eisert, H. J. Briegel. Schmidt measure as a tool for quantifying multiparticle entanglement[J]. Phys Rev A. 2001, 64(2): 022306
[104] M. Hein. Entanglement in Graph States[D]. 博士学位论文， University of Innsbruck, Austria, 2005
[105] O. Guhne, G. Toth, P. Hyllus, H. J. Briegel. Bell inequalities for graph states[J]. Phys Rev Lett. 2005, 95(12): 120405
[106] G. Toth, O. Guhne. Detecting genuine multipartite entanglement with two local measurements[J]. Phys Rev Lett. 2005, 94(6):060501
[107] G. Toth, O. Guhne, H. J. Briegel. Two-setting Bell inequalities for graph states[J]. Phys Rev A. 2006, 73(2):022303
[108] 张维迎．《博弈论与信息经济学》[M]．上海人民出版社，1996
[109] 施锡铨．《博弈论》[M]．上海财经大学出版社，2000
[110] M. A. Nowak, K. Sigmund.[J]. Nature. 1999, 398: 367
[111] J. Von Neumann, O. Morgenstern. Theory of Games and Economic Behavior[M]. Princeton University Press, Second Ed., 1947
[112] Richard Cleve, Harry Buhrman. Substituting quantum entanglement for communication[J]. Phys Rev A (Atomic, Molecular, and Optical Physics). 1997, 56(2): 1201-1204
[113] Artur K. Ekert. Quantum cryptography based on Bell's theorem[J]. Phys Rev Lett. 1991, 67(6): 661-663
[114] David A. Meyer. Quantum Strategies[J]. Phys Rev Lett. 1999, 82(5): 1052-1055
[115] D. A. Meyer. Quantum Games and Quantum Algorithms[J]. quant-ph/0004092, to appear in the AMS Contemporary Mathematics volume: Quantum Computation and Quantum Information Science. 2000
[116] Jens Eisert, Martin Wilkens, Maciej Lewenstein. Quantum Games and Quantum Strategies[J]. Phys Rev Lett. 1999, 83(15): 3077-3080
[117] Simon C. Benjamin, Patrick M. Hayden. Multiplayer quantum games[J]. Phys Rev A (Atomic, Molecular, and Optical Physics). 2001, 64(3): 030301 (pages 4)
[118] Jiangfeng Du, Hui Li, Xiaodong Xu, Xianyi Zhou, Rongdian Han. Entanglement enhanced multiplayer quantum games[J]. Phys Lett A. 2002/9/30, 302(5-6):229-233
[119] Jiangfeng Du, Xiaodong Xu, Hui Li, Xianyi Zhou, Rongdian Han. Entanglement playing a dominating role in quantum games[J]. Phys Lett A. 2001/10/8, 289(1-2): 9-15
[120] Jiangfeng Du, Hui Li, Xiaodong Xu, Mingjun Shi, Jihui Wu, Xianyi Zhou, Rongdian Han. Experimental Realization of Quantum Games on a Quantum Computer[J]. Phys Rev Lett. 2002, 88(13): 137902 (pages 4)
[121] 杜江峰，李卉，许晓栋．《量子力学新进展》(第三辑)第五章《量子博弈论》[M]．清华大学出版社 曾谨言 龙桂鲁 裴寿镛主编，2003年10月
[122] W. B. Arthur.[J]. Am Econ Assoc Papers and Proc. 1994, 84: 406
[123] Q. Chen, W. Yi, J. T. Liu, K. L. Wang. N-player quantum minority game[J]. Phys Lett A. 2004, 327(2-3): 98-102
[124] R. Raussendorf, D. E. Browne, H. J. Briegel. The one-way quantum computer-a nonnetwork model of quantum computation[J]. J Mod Optics. 2002, 49(8): 1299-1306
[125] R. Raussendorf, D. E. Browne, H. J. Briegel. Measurement-based quantum computation on cluster states[J]. Phys Rev A. 2003, 68(2):022312
[126] M. A. Nielsen. Cluster-state quantum computation[J]. Rep Math Phys. 2006, 57(1):147-161
[127] S. R. Clark, C. M. Alves, D. Jaksch. Efficient generation of graph states for quantum computation[J]. New J Phys. 2005, 7: 124
[128] M. Borhani, D. Loss. Cluster states from Heisenberg interactions[J]. Phys Rev A. 2005, 71(3): 034308
[129] M. Mhalla, S. Perdrix. Complexity of Graph State Preparation[J]. ArXiv Quantum Physics e-prints. Dec. 2004. arXiv: quant-ph/0412071
[130] Raussendorf R. Briegel H. J., Schenzle A. Optical lattices as a playground for studying multiparticle entanglement[M]. Springer, 2002
[131] D. Jaksch, H. J. Briegel, J. I. Cirac, C. W. Gardiner, P. Zoller. Entanglement of atoms via cold controlled collisions[J]. Phys Rev Lett. 1999, 82(9): 1975-1978
[132] H. J. Briegel, T. Calarco, D. Jaksch, J. I. Cirac, P. Zoller. Quantum computing with neutral atoms[J]. J Mod Optics. 2000, 47(2-3): 415-451
[133] L. M. Duan, E. Demler, M. D. Lukin. Controlling spin exchange interactions of ultracold atoms in optical lattices[J]. Phys Rev Lett. 2003, 91(9): 090402
[134] D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, P. Zoller. Cold bosonic atoms in optical lattices[J]. Phys Rev Lett. 1998, 81(15): 3108-3111
[135] M. Greiner, O. Mandel, T. W. Hansch, I. Bloch. Collapse and revival of the matter wave field of a Bose-Einstein condensate[J]. Nature. 2002, 419(6902):51-54
[136] M. Greiner, O. Mandel, T. Esslinger, T. W. Hansch, I. Bloch. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms[J]. Nature. 2002, 415(6867): 39-44
[137] O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hansch, I. Bioch. Controlled collisions for multi-particle entanglement of optically trapped atoms[J]. Nature. 2003, 425(6961):937 -940
[138] P. Rabl, A. J. Daley, P. O. Fedichev, J. I. Cirac, P. Zoller. Defect-suppressed atomic crystals in an optical lattice[J]. Phys Rev Lett. 2003,91(11):110403
[139] K. G. H. Vollbrecht, E. Solano, J. I. Cirac. Ensemble quantum computation with atoms in periodic potentials[J]. Phys Rev Lett. 2004, 93(22):220502
[140] E. Knill, R. Laflamme, G. J. Milburn. A scheme for efficient quantum computation with linear optics[J]. Nature. 2001, 409(6816):46- 52
[141] N. Yoran, B. Reznik. Deterministic linear optics quantum computation with single photon qubits[J]. Phys Rev Lett. 2003, 91(3):037903
[142] M. A. Nielsen. Optical quantum computation using cluster states[J]. Phys Rev Lett. 2004, 93(4):040503
[143] D. E. Browne, T. Rudolph. Resource-efficient linear optical quantum computation[J]. Phys Rev Lett. 2005, 95(1):010501
[144] T. C. Ralph, A. J. F. Hayes, A. Gilchrist. Loss-tolerant optical qubits[J]. Phys Rev Lett. 2005, 95(10): 100501
[145] A. N. Zhang, C. Y. Lu, X. Q. Zhou, Y. A. Chen, Z. Zhao, T. Yang, J. W. Pan. Experimental construction of optical multiqubit cluster states from Bell states[J]. Phys Rev A. 2006, 73(2):022330
[146] P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, A. Zeilinger. Experimental one-way quantum computing[J]. Nature. 2005, 434(7030): 169 - 176
[147] S. D. Barrett, P. Kok. Efficient high-fidelity quantum computation using matter qubits and linear optics[J]. Phys Rev A. 2005, 71(6):060310
[148] S. C. Benjamin, J. Eisert, T. M. Stace. Optical generation of matter qubit graph states[J]. New J Phys. 2005,7:194
[149] Y. L. Lim, A. Beige, L. C. Kwek. Repeat-until-success linear optics distributed quantum computing[J]. Phys Rev Lett. 2005, 95(3):030505
[150] Y. L. Lim, S. D. Barrett, A. Beige, P. Kok, L. C. Kwek. Repeat-until-success quantum computing using stationary and flying qubits[J]. Phys Rev A. 2006, 73(1):012304
[151] X. L. Zhang, M. Feng, K. L. Gao. Cluster-state preparation and multipartite entanglement analyzer with fermions[J]. Phys Rev A. 2006, 73(1):014301
[152] L. M. Duan, R. Raussendorf. Efficient quantum computation with probabilistic quantum gates[J]. Phys Rev Lett. 2005, 95(8):080503
[153] Q. Chen, J. H. Cheng, K. L. Wang, J. F. Du. Efficient construction of two-dimensional cluster states with probabilistic quantum gates[J]. Phys Rev A. 2006. arXiv:quant-ph/0507066
[154] M. Hein, W. Dur, H. J. Briegel. Entanglement properties of multipartite entangled states under the influence of decoherence[J]. Phys Rev A. 2005, 71(3):032350
[155] HJ Briegel, BG Englert. Quantum optical mater-quations - the use of damping bases[J]. Phys Rev A. 1993, 47(4):3311 - 3329
[156] W Dur, JI Cirac. Activating bound entanglement in multiparticle systems[J]. Phys Rev A. 2000, 62(2):022302
[157] W Dur, JI Cirac. Classification of multiqubit mixed states: Separability and distillability properties[J]. Phys Rev A. 2000, 61(4):042314
[158] W Dur, JI Cirac. Multiparticle entanglement and its experimental detection[J]. J Phys A: Math Gen. 2001, 34(35):6837 - 6850
[159] M Horodecki, P Horodecki, R Horodecki. Inseparable two spin-1/2 density matrices can be distilled to a singlet form[J]. Phys Rev Lett. 1997,78(4):574 - 577
[160] A Peres. Separability criterion for density matrices[J]. Phys Rev Lett. 1996, 77(8): 1413 -1415
[161] M Horodecki, P Horodecki, R Horodecki. Separability of mixed states: Necessary and sufficient conditions[J]. Phys Lett A. 1996, 223(1-2):1 - 8