多量子位纠缠态的制备
|
摘要
建立在量子力学基础之上的量子信息学,是一门利用量子力学原理解决经典信息学和经典计算机所不能解决的问题的学科,它可以突破现代信息技术的物理极限,开拓新的信息发展空间。由于在量子信息学中,信息的存储、表示、提取等都离不开量子态及其演化过程,而量子纠缠态具有独特的量子关联特性,因此量子纠缠在量子信息学中起着非常重要的作用,是量子信息学发展的重要基础。然而,信息在制备、传输及存储过程中不可避免地要受到环境的影响并与环境发生相互作用,因此会出现量子退相干现象,使信息遭到破坏。因此,量子纠缠和量子相干是量子信息学中的两个重要物理资源。对于如何建立量子纠缠,控制量子态的演化,并且保持量子相干性问题的研究是量子信息理论的重要课题。在纠缠态制备方面,即在建立量子纠缠方面,两量子位纠缠态已经被广泛研究了,而多量子位纠缠比两量子位纠缠更适用于量子克隆、量子纠错、量子隐形传输和量子密集编码,是量子计算和量子信息处理的重要资源。本文主要利用腔QED系统、腔辅助光子散射系统及固态系统提出了几种多量子位纠缠态制备的理论方案,分析了各个方案的可行性,并且,讨论了如何消除量子退相干的影响。
量子退相干现象的存在会破坏量子纠缠,因此,了解纠缠的演化特性对我们更好地控制纠缠,避免量子退相干的影响是非常重要的。我们首先对分别处于两个失谐腔中的两个远距离原子之间的纠缠演化做了初步探讨,比较了Concurrence和Negativity对纠缠的评价。结果表明,两原子的纠缠演化出现纠缠突然死亡现象。当两个腔场的粒子数相等时,随着粒子数的增加,纠缠死亡和纠缠产生的频率加快,同时Concurrence的振幅也出现规则的振荡且振荡频率变慢。当两个腔场的粒子数不等时,Concurrence的最大值明显衰减,并且,Concurrence的振幅不再出现规则振荡现象。此外,我们发现纠缠死亡时间依赖于初始纠缠。
基于腔QED技术,我们提出了利用一个Λ型原子和两个二能级原子依次与双模腔的两个模或一个模发生相互作用制备三原子W态和三原子GHZ态的理论方案。在方案中,三个原子依次进入腔中与腔场发生相互作用,通过适当地选择相互作用时间可以很方便地制备三原子W态和三原子GHZ态。在考虑场衰减和原子自发辐射时,只要原子和腔发生强耦合相互作用,我们也可以得到高保真的纠缠态。
基于腔辅助光子散射技术,我们首次提出了制备χ型四原子纠缠态∣χ00?3214的理论方案。在方案中,我们利用原子和光子间控制反转门的实现,在仅使用了若干简单的线性光学元件和一个传统光学探测器的情况下成功地制备了χ型四原子纠缠态∣χ00?3214。由于光子与环境之间的相互作用很弱,适合于远距离的量子信息传输,只要没有光子损失,我们就可以成功地制备χ型四原子纠缠态∣χ00?3214。
量子退相干现象的存在,使量子纠缠受到破坏进而使通信出现噪声或使计算结果出现误差。为了克服退相干,我们可以将量子位编码在Hilbert的一个子空间——无退相干子空间(DFS),这样噪声和误差就会被消除。因此,我们同样基于腔辅助光子散射技术提出了制备任意四原子纠缠DFS态的理论方案。在方案中,我们只需方便地调节一个半波片的倾角就可以得到任意四原子纠缠DFS态。
与腔QED系统和线性光学系统相比,固态量子位之间的纠缠更稳定,更容易建立多量子位纠缠,因此,基于自旋网络这一固态系统,我们提出了制备多量子位图态的理论方案。首先,通过XY相互作用实现了χSWAP门,然后,我们利用χSWAP门及单量子位旋转操作制备了在局域幺正变换和图形同构情况下三种典型的不等价的四量子位图态和四种典型的不等价的五量子位图态。与基于传统控制非门和控制相位门制备纠缠态的方案相比,我们的方案利用自旋系统的χSWAP门,相互作用时间短,且纠缠能力强,可以有效地避免量子退相干的影响,并且更适合于可扩展量子计算。
Quantum information, based on quantum mechanics, is a subject using quantumtheory of microscopic particles to resolve problems which can not be resolved by clas-sical information and classical computation. It can break through physical limitations ofcurrent information technology to exploit new functions of information. In quantum in-formation processing, storing, denoting and extracting of information are dependent onquantum states and their evolution. Because quantum entanglement is associated with thepeculiar nonclassical correlations, it plays an important role in quantum information pro-cessing and is at the heart of quantum information. Quantum system, in which quantuminformation is prepared, transmitted and stored, often interacts with environment, whichresults the loss of information, and this phenomenon is called decoherence. Therefore,quantum entanglement and quantum coherence are important resources of quantum infor-mation. Thus, the problems about how to prepare entangled state, control the evolutionof quantum state and keep quantum coherence have become the most important subjectof quantum physics. For the preparation of entangled states, the cases of two qubit are in-vestigated extensively. However, multi-qubit entangled states have more advantages thanthe two qubit entangled states in their applications in quantum cloning, teleportation anddense coding, so in this paper, we mainly study the theoretical schemes for preparing afew multi-qubit entangled states by using cavity QED technology, cavity-assisted photonscattering technology and spin network, respectively, and analyze the feasibility of theschemes, then discuss how to eliminate the in?uence of quantum decoherence.
Because quantum decoherence can destroy quantum entanglement, improving ourunderstanding on entanglement dynamics and properties is necessary for manipulatingentanglement and resisting the in?uence of decoherence. Therefore, we make a prelim-inary investigation of the entanglement dynamics via Concurrence of two distant atomsinteracting off-resonantly with two cavity fields, respectively, and a comparison betweenConcurrence and Negativity about their evaluation on entanglement. We show that theevolution of entanglement has sudden death and sudden birth phenomena and with theincreasing of photon number in the two cavities, the alternative frequencies of suddendeath and sudden birth get fast and the amplitude of Concurrence oscillates regularly with oscillation frequency becoming slow when the cavity fields have same photon numbers.Whereas, the maximum of Concurrence declines and the amplitude of Concurrence os-cillates irregularly when the two cavity fields have different photon numbers. In addition,we find that the length of death time is dependent on the degree of entanglement of theinitial state.
In cavity QED, we propose two scheme for preparing the three-atom W state andthe GHZ state respectively, with oneΛ-type atom and two two-level atoms interactingresonantly with two modes or one mode of a two-mode field in turns. By controlling theevolution time of quantum state appropriately, we can obtain the three-atom W state andthree-atom GHZ state. When we consider the atomic spontaneous emission and cavitydecay, we can obtain high-fidelity entanglement as long as the schemes work beyond thestrong-coupling regime.
With cavity-assisted photon scattering technology, we propose a theoretical schemefor generating a newχ-type four-atom entangled state∣χ00?3214 for the first time. In thescheme, we generate successfully theχ-type four-atom entangled states∣χ00?3214 by usingthe controlled phase ?ip gate with atom and single-photon, simple linear optics elements,and a conventional photon detector. Because the photon has weak interaction with theenvironment, it is suitable for distant information transmission, so the state∣χ00?3214 canbe generated with probability 1 as long as there is no photon loss.
The decoherence precesses caused by the in?uence of the environment often easilydestroy entanglement and furthermore cause noise in the communication or errors in theoutcomes of computation. In order to overcome decoherence, we may encode logicalqubits into a subspace of the whole Hilbert space, a decoherence-free subspace (DFS),thus the noise and errors can be resisted efficiently. Similarly, by using cavity-assistedphoton scattering technology we propose a scheme for generating arbitrary four-atomentangled DFS states. By conveniently tuning the titled angle of one half-wave plate, wecan obtain arbitrary four-atom entangled DFS states with probability 1 as long as there isno photon loss.
Compared with cavity QED and linear optics systems, solid-state qubit can be ex-tended more easily for generating multi-qubit entangled states. Based on spin networks,we propose efficient schemes for preparing multi-qubit graph states. At first, we deriveχSWAP gate for XY interaction, and then we prepare the three classical types of four- qubit graph states inequivalent each other under local unitary transformations and graphisomorphism, and four classical types of five-qubit graph states inequivalent, by usingχSWAP-gate and some single-qubit rotations. By usingχSWAP gate for spin networks,our method makes the generation of multipartite entangled graph states more efficient thanthe ones based on conventional controlled-NOT and controlled phase ?ip gate for solid-state devices, due to its short interaction time and its strong entanglement forχSWAP-gatein solid-state system, so it can overcome the in?uence of quantum decoherence and facil-itates the scalable quantum computation.
量子退相干现象的存在会破坏量子纠缠,因此,了解纠缠的演化特性对我们更好地控制纠缠,避免量子退相干的影响是非常重要的。我们首先对分别处于两个失谐腔中的两个远距离原子之间的纠缠演化做了初步探讨,比较了Concurrence和Negativity对纠缠的评价。结果表明,两原子的纠缠演化出现纠缠突然死亡现象。当两个腔场的粒子数相等时,随着粒子数的增加,纠缠死亡和纠缠产生的频率加快,同时Concurrence的振幅也出现规则的振荡且振荡频率变慢。当两个腔场的粒子数不等时,Concurrence的最大值明显衰减,并且,Concurrence的振幅不再出现规则振荡现象。此外,我们发现纠缠死亡时间依赖于初始纠缠。
基于腔QED技术,我们提出了利用一个Λ型原子和两个二能级原子依次与双模腔的两个模或一个模发生相互作用制备三原子W态和三原子GHZ态的理论方案。在方案中,三个原子依次进入腔中与腔场发生相互作用,通过适当地选择相互作用时间可以很方便地制备三原子W态和三原子GHZ态。在考虑场衰减和原子自发辐射时,只要原子和腔发生强耦合相互作用,我们也可以得到高保真的纠缠态。
基于腔辅助光子散射技术,我们首次提出了制备χ型四原子纠缠态∣χ00?3214的理论方案。在方案中,我们利用原子和光子间控制反转门的实现,在仅使用了若干简单的线性光学元件和一个传统光学探测器的情况下成功地制备了χ型四原子纠缠态∣χ00?3214。由于光子与环境之间的相互作用很弱,适合于远距离的量子信息传输,只要没有光子损失,我们就可以成功地制备χ型四原子纠缠态∣χ00?3214。
量子退相干现象的存在,使量子纠缠受到破坏进而使通信出现噪声或使计算结果出现误差。为了克服退相干,我们可以将量子位编码在Hilbert的一个子空间——无退相干子空间(DFS),这样噪声和误差就会被消除。因此,我们同样基于腔辅助光子散射技术提出了制备任意四原子纠缠DFS态的理论方案。在方案中,我们只需方便地调节一个半波片的倾角就可以得到任意四原子纠缠DFS态。
与腔QED系统和线性光学系统相比,固态量子位之间的纠缠更稳定,更容易建立多量子位纠缠,因此,基于自旋网络这一固态系统,我们提出了制备多量子位图态的理论方案。首先,通过XY相互作用实现了χSWAP门,然后,我们利用χSWAP门及单量子位旋转操作制备了在局域幺正变换和图形同构情况下三种典型的不等价的四量子位图态和四种典型的不等价的五量子位图态。与基于传统控制非门和控制相位门制备纠缠态的方案相比,我们的方案利用自旋系统的χSWAP门,相互作用时间短,且纠缠能力强,可以有效地避免量子退相干的影响,并且更适合于可扩展量子计算。
Quantum information, based on quantum mechanics, is a subject using quantumtheory of microscopic particles to resolve problems which can not be resolved by clas-sical information and classical computation. It can break through physical limitations ofcurrent information technology to exploit new functions of information. In quantum in-formation processing, storing, denoting and extracting of information are dependent onquantum states and their evolution. Because quantum entanglement is associated with thepeculiar nonclassical correlations, it plays an important role in quantum information pro-cessing and is at the heart of quantum information. Quantum system, in which quantuminformation is prepared, transmitted and stored, often interacts with environment, whichresults the loss of information, and this phenomenon is called decoherence. Therefore,quantum entanglement and quantum coherence are important resources of quantum infor-mation. Thus, the problems about how to prepare entangled state, control the evolutionof quantum state and keep quantum coherence have become the most important subjectof quantum physics. For the preparation of entangled states, the cases of two qubit are in-vestigated extensively. However, multi-qubit entangled states have more advantages thanthe two qubit entangled states in their applications in quantum cloning, teleportation anddense coding, so in this paper, we mainly study the theoretical schemes for preparing afew multi-qubit entangled states by using cavity QED technology, cavity-assisted photonscattering technology and spin network, respectively, and analyze the feasibility of theschemes, then discuss how to eliminate the in?uence of quantum decoherence.
Because quantum decoherence can destroy quantum entanglement, improving ourunderstanding on entanglement dynamics and properties is necessary for manipulatingentanglement and resisting the in?uence of decoherence. Therefore, we make a prelim-inary investigation of the entanglement dynamics via Concurrence of two distant atomsinteracting off-resonantly with two cavity fields, respectively, and a comparison betweenConcurrence and Negativity about their evaluation on entanglement. We show that theevolution of entanglement has sudden death and sudden birth phenomena and with theincreasing of photon number in the two cavities, the alternative frequencies of suddendeath and sudden birth get fast and the amplitude of Concurrence oscillates regularly with oscillation frequency becoming slow when the cavity fields have same photon numbers.Whereas, the maximum of Concurrence declines and the amplitude of Concurrence os-cillates irregularly when the two cavity fields have different photon numbers. In addition,we find that the length of death time is dependent on the degree of entanglement of theinitial state.
In cavity QED, we propose two scheme for preparing the three-atom W state andthe GHZ state respectively, with oneΛ-type atom and two two-level atoms interactingresonantly with two modes or one mode of a two-mode field in turns. By controlling theevolution time of quantum state appropriately, we can obtain the three-atom W state andthree-atom GHZ state. When we consider the atomic spontaneous emission and cavitydecay, we can obtain high-fidelity entanglement as long as the schemes work beyond thestrong-coupling regime.
With cavity-assisted photon scattering technology, we propose a theoretical schemefor generating a newχ-type four-atom entangled state∣χ00?3214 for the first time. In thescheme, we generate successfully theχ-type four-atom entangled states∣χ00?3214 by usingthe controlled phase ?ip gate with atom and single-photon, simple linear optics elements,and a conventional photon detector. Because the photon has weak interaction with theenvironment, it is suitable for distant information transmission, so the state∣χ00?3214 canbe generated with probability 1 as long as there is no photon loss.
The decoherence precesses caused by the in?uence of the environment often easilydestroy entanglement and furthermore cause noise in the communication or errors in theoutcomes of computation. In order to overcome decoherence, we may encode logicalqubits into a subspace of the whole Hilbert space, a decoherence-free subspace (DFS),thus the noise and errors can be resisted efficiently. Similarly, by using cavity-assistedphoton scattering technology we propose a scheme for generating arbitrary four-atomentangled DFS states. By conveniently tuning the titled angle of one half-wave plate, wecan obtain arbitrary four-atom entangled DFS states with probability 1 as long as there isno photon loss.
Compared with cavity QED and linear optics systems, solid-state qubit can be ex-tended more easily for generating multi-qubit entangled states. Based on spin networks,we propose efficient schemes for preparing multi-qubit graph states. At first, we deriveχSWAP gate for XY interaction, and then we prepare the three classical types of four- qubit graph states inequivalent each other under local unitary transformations and graphisomorphism, and four classical types of five-qubit graph states inequivalent, by usingχSWAP-gate and some single-qubit rotations. By usingχSWAP gate for spin networks,our method makes the generation of multipartite entangled graph states more efficient thanthe ones based on conventional controlled-NOT and controlled phase ?ip gate for solid-state devices, due to its short interaction time and its strong entanglement forχSWAP-gatein solid-state system, so it can overcome the in?uence of quantum decoherence and facil-itates the scalable quantum computation.
引文
1李承祖,黄明球,陈平形,等.量子通信和量子计算[M].第1版.,长沙:国防科技大学出版社, 2000.
2 P. Benioff. The Computer as a Physical System: A Microscopic Quantum Mechan-ical Hamlitonian Model of Computers as Represented by Turing Machines[J]. J.Stat. Phys., 1980, 22(5):563–591.
3 R. P. Feynman. Simulating Physics with Computers[J]. Int. J. Theor. Phys, 1982,21(6):467–488.
4 W. K. Wootters, W. H. Zurek. A Single Quantum Cannot Be Cloned[J]. Nature,1992, 299(5886):802–803.
5 M. A. Nielsen, I. L. Chuang. Quantum Computation and Quantum Information[M].
276 ed., Cambridge: Cambridge University Press, 2000:171–276.
6杨涛,潘建伟.量子信息技术的新进展[J].中国科学院院刊, 2004, 19(5):355–357.
7张国锋.量子纠缠的若干问题研究[D].山西:山西大学, 2004:6–9.
8 C. H. Bennett, F. Bessette, G. Brassard, et al. Experimental Quantum Cryptogra-phy[J]. J. Cryptology, 1992, 5(1):3–28.
9 J. Kempe. Approaches to Quantum Error Correction[C]//Progress in MathematicalPhysics Series. Birhaeuser, 2006:85–123.
10 C. H. Bennett, G. Brassard, C. Crepeau, et al. Teleporting an Unknown QuantumState via Dual Classical and Einstein-podolsky-rosen Channels[J]. Phys. Rev. Lett.,1993, 70(13):1895–1899.
11 A. K. Ekert. Quantum Cryptography Based on Bell’s Theorem[J]. Phys. Rev. Lett,1991, 67(6):661–663.
12 A. Steane. Quantum Computing[J]. Rep. Prog. Phys., 1998, 61(2):117–173.
13 K. Mattle, H. Weinfurter, P. G. Kwiat, et al. Dense Coding in Experimental Quan-tum Communication[J]. Phys. Rev. Lett., 1996, 79(25):4656–4659.
14 P. W. Shor. Algorithms for Quantum Computations: Discrete Logarithms and Fac-toring[C]//Proc. 35th Annu. Sym. Found. Comput. Science. Los Alamitos: IEEEComputer Society Press, 1994:124–134.
15 A. Ekert, R. Jozsa. Quantum Computation and Shor’s Factoring Algorithm[J]. Pev.Mod. Phys., 1996, 68(3):733–753.
16 L. K. Grover. Quantum Mechanics Helps in Searching for a Needle in aHaystack[J]. Phys. Rev. Lett, 1997, 79(2):325–328.
17 G. Rigolin. Quantum Teleportation of an Arbitrary Two-qubit State and its Relationto Multipartite Entanglement[J]. Phys. Rev. A, 2005, 71:032303–5.
18 S. B. Zheng, G. C. Guo. Scheme for Atomic-state Teleportation between Two BadCavities[J]. Phys. Rev. A, 2006, 73(3):032329–5.
19 Y. Yeo, W. K. Chua. Teleportation and Dense Coding with Genuine MultipartiteEntanglement[J]. Phys. Rev. Lett., 2006, 96(6):060502–4.
20 G. Gordon, G. Rigolin. Generalized Teleportation Protocol[J]. Phys. Rev. A, 2006,73(4):042309–4.
21 S. B. Zheng. State-independent Teleportation of an Atomic State between TwoCavities[J]. Phys. Rev. A, 2008, 77(4):044303–4.
22 D. Bouwmeester, J. W. Pan, K. Mattle, et al. Experimental Quantum Teleporta-tion[J]. Nature(London), 1997, 390(6660):575–579.
23 M. A. Nielsen, E. Knill, R. La?amme. Complete Quantum Teleportation UsingNuclear Magnetic Resonance[J]. Nature, 1998, 396(6706):52–55.
24 J. W. Pan, M. Daniell, S. Gasparoni, et al. Experimental Demonstration of Four-photon Entanglement and High-fidelity Teleportation[J]. Phys. Rev. Lett., 2001,86(20):4435–4438.
25 Z. Zhao, A. Y. Chen, A. N. Zhang, et al. Experimental Demonstration ofFive-photon Entanglement and Open-destination Teleportation[J]. Nature, 2004,430(6995):54–58.
26 Q. Zhang, A. Goebel, C. Wagenknecht, et al. Experimental Quantum Teleportationof a Two-qubit Composite System[J]. Nature Phys., 2006, 2(10):678–682.
27 Y. A. Chen, S. Chen, Z. S. Yuan, et al. Memory-built-in Quantum Teleportationwith Photonic and Atomic Qubits[J]. Nature Phys., 2008, 4(2):103–107.
28 S. Olmschenk, D. N. Matsukevich, P. Maunz, et al. Quantum Teleportation betweenDistant Matter Qubits[J]. Science, 2009, 323(5913):486–489.
29 X. M. Jin, J. G. Ren, B. Yang, et al. Experimental Free-space Quantum Teleporta-tion[J]. Nature Photon., 2010, 4(6):376–380.
30 C. H. Bennett, S. J. Wiesner. Communication via One and Two-particle Operatorson Einstein-podolsky-rosen States[J]. Phys. Rev. Lett., 1992, 69(20):2881–2884.
31 X. M. Fang, X. W. Zhu, M. Feng, et al. Experimental Implementation of DenseCoding Using Nuclear Magnetic Resonance[J]. Phys. Rev. A, 2000, 61(2):022307–5.
32 J. Zhang, K. Peng. Quantum Teleportation and Dense Coding by Means of BrightAmplitude-squeezed Light and Direct Measurement of a Bell State[J]. Phys. Rev.A, 2000, 62(6):064302–4.
33 J. C. Hao, C. F. Li, G. C. Guo. Controlled Dense Coding Using the Greenberger-horne-zeilinger State[J]. Phys. Rev. A, 2001, 63(5):054301–3.
34 X. S. Liu, G. L. Long, D. M. Tong, et al. General Scheme for Superdense Codingbetween Miltiparties[J]. Phys. Rev. A, 2002, 65(2):022304–4.
35 L. Ye, L. B. Yu. Scheme for Implementing Quantum Dense Coding Using TripartiteEntanglement in Cavity Qed[J]. Phys. Lett. A, 2005, 346(5-6):330–336.
36 S. Mozes, J. Oppenheim, B. Reznik. Deterministic Dense Coding with PartiallyEntangled States[J]. Phys. Rev. A, 2005, 71(1):012311–7.
37 G. M. Wang, M. S. Ying. Deterministic Distributed Dense Coding with StabilizerStates[J]. Phys. Rev. A, 2008, 77(3):032306–10.
38 C. H. Bennett, G. Brassard. Quantum Cryptography: Public Key Distribution andCoin Tossing[C]//Proceedings of IEEE International Conference on Computers,Systems and Signal Processing. Bangalore India, 1984:175–179.
39 K. Horodecki, D. Leung, H. K. Lo, et al. Quantum Key Distribution Based on Arbi-trarily Weak Distillable Entangled States[J]. Phys. Rev. Lett., 2006, 96(7):070501–4.
40 X. F. Ma, C. H. F. Fung, H. K. Lo. Quantum Key Distribution with EntangledPhoton Sources[J]. Phys. Rev. A, 2007, 76(1):012307–10.
41 A. Ling, M. P. Peloso, I. Marcikic, et al. Experimental Quantum Key DistributionBased on a Bell Test[J]. Phys. Rev. A, 2008, 78(2):020301(R)–4.
42 S. J. D. Phoenix, S. M. Barnett. Non-local Interatomic Correlations in the Micro-master[J]. J. Mod. Opt., 1993, 40(6):979–983.
43 I. K. Kudryavtsev, P. L. Knight. Atomic Entanglement and Bell’s Inequality[J]. J.Mod. Opt., 1993, 40(9):1673–1679.
44 J. I. Cirac, P. Zoller. Preparation of Macroscopic Superpositions in Many-atomSystems[J]. Phys. Rev. A, 1994, 50(4):R2799–R2802.
45 E. Haglay, X. Ma??tre, G. Nogues, et al. Generation of Einstein-podolsky-rosen Pairsof Atoms[J]. Phys. Rev. Lett., 1997, 79(1):1–5.
46 S. B. Zheng, G. C. Guo. Efficient Scheme for Two-atom Entanglement and Quan-tum Information Processing in Cavity Qed[J]. Phys. Rev. Lett., 2000, 85(11):2392–2395.
47 S. Osnaghi, P. Bertet, A. Auffeves, et al. Coherent Control of an Atomic Collisionin a Cavity[J]. Phys. Rev. Lett., 2001, 87(3):037902–4.
48 L. Ye, L. B. Yu, G. C. Guo. Generation of Entangled States in Cavity Qed[J]. Phys.Rev. A, 2005, 72(3):034304–4.
49 Y. F. Xiao, X. B. Zou, G. C. Guo. Generation of Atomic Entangled States withSelective Resonant Interaction in Cavity Quantum Electrodynamics[J]. Phys. Rev.A, 2007, 75(1):012310–5.
50 S. B. Li. Generation of Maximally Entangled Mixed States of Two Atomsvia On-resonance Asymmetric Atom-cavity Couplings[J]. Phys. Rev. A, 2007,75(5):054304–4.
51 P. J. D. Reis, S. S. Sharma. Generation of Field-mediated Three-qubit EntangledState Shared by Alice and Bob[J]. Phys. Rev. A, 2009, 79(1):012326–9.
52 J. I. Cirac, P. Zoller. Quantum Computations with Cold Trapped Ions[J]. Phys. Rev.Lett., 1995, 74(20):4091–4094.
53 A. S. Parkins, H. J. Kimble. Quantum State Transfer between Motion and Light[J].J. Opt. B:Quantum Semiclassical Opt., 1999, 1(4):496–504.
54 A. S. Parkins, E. larsabal. Preparation and Light-mediated Distribution of MotionalState Entanglement[J]. Phys. Rev. A, 2000, 63(1):012304–17.
55 A. Peng, A. S. Parkins. Motion-light Parametric Amplifier and Entanglement Dis-tributor[J]. Phys. Rev. A, 2002, 65(6):062323–8.
56 G. X. Li, H. T. Tan, S. P. Wu. Motional Entanglement for Two Trapped Ions inCascaded Optical[J]. Phys. Rev. A, 2004, 70(6):064301–4.
57 G. X. Li, S. P. Wu, G. M. Huang. Generation of Entanglement and Squeezing in theSystem of Two Ions Trapped in a Cavity[J]. Phys. Rev. A, 2005, 71(6):063817–9.
58 G. X. Li, S. P. Wu. Effect of Vibrational Heating on the Entangled Fiald from anIon Trapped in a Bimodal Cavity[J]. Phys. Rev. A, 2005, 72(6):064304–4.
59 G. Morigi, J. Eschner, S. Mancini, et al. Entangled Light Pulses from Single ColdAtoms[J]. Phys. Rev. Lett., 2006, 96(2):023601–4.
60 S. B. Zheng. Generation of Entangled States of Multiple Trapped Ions in ThermalMotion[J]. Phys. Rev. A, 2004, 70(4):045804–3.
61 G. X. Li. Generation of Pure Multipartite Entangled Vibrational States for IonsTrapped in a Cavity[J]. Phys. Rev. A, 2006, 74(5):055801–4.
62 A. Retzker, E. Solano, B. Reznik. Tavis-cummings Model and Collective Multi-qubit Entanglement in Trapped Ions[J]. Phys. Rev. A, 2007, 75(2):022312–6.
63 I. E. Linington, N. V. Vitanov. Decoherence-free Preparation of Dicke Sates ofTrapped Ions by Collective Stimulated Raman Adiabatic Passage[J]. Phys. Rev. A,2008, 77(6):062327–14.
64 X. W. Wang, G. J. Yang. Generation and Discrimination of a Type of Four-partiteEntangled State[J]. Phys. Rev. A, 2008, 78(2):024301–4.
65孙利群,王佳,田芊,等.自发参量下转换双光子场应用研究进展[J].物理,2000, 29(12):727–731.
66 P. G. Kwiat, E. Waks, A. G. White, et al. Ultrabright Source of Polarization-entangled Photons[J]. Phys. Rev. A, 1999, 60(2):R773–R776.
67 J. W. Pan, D. Bouwmeester, M. Daniell, et al. Experimental Test of QuantumNonlocality in Three-photon Greenberger-horne-zeilinger Entanglement[J]. Na-ture, 2000, 403(6769):515–519.
68 X. B. Zou, J. Shu, G. C. Guo. Simple Scheme for Generating Four-photonPolarization-entangled Decoherence-free States Using Spontaneous ParametricDown-conversions[J]. Phys. Rev. A, 2006, 73(5):054301–4.
69 B. Liu, Z. Y. Ou. Engineering Multiphoton Entangled States by Quantum Interfer-ence[J]. Phys. Rev. A, 2006, 74(3):035802–3.
70 Y. X. Gong, X. B. Zou, X. L. Niu, et al. Generation of Arbitrary Foue-hoton Polarization-entangled Decoherence-free Sates[J]. Phys. Rev. A, 2008,77(4):042317–5.
71 C. Y. Lu, X. Q. Zhou, O. Gu¨hne, et al. Experimental Entanglement of Six Photonsin Gragh States[J]. Nature Phys., 2007, 3(2):91–95.
72 S. Y. Baek, Y. H. Kim. Generating Entangled States of Two Ququarts Using LinearOptical Elements[J]. Phys. Rev. A, 2007, 75(3):034309–4.
73 K. Lemr, J. Fiura′sˇek. Preparation of Entangled States of Two Photons in SeveralSpatiel Modes[J]. Phys. Rev. A, 2008, 77(2):023802–8.
74 B. Stefanie, C. Gunther, Z. Anton, et al. Heralded Generation of Entangled PhotonPairs[J]. Nature Photon., 2010, 4(8):553–556.
75 J. Cho, H. W. Lee. Generation of Atomic Cluster States Through the Cavity Input-output Process[J]. Phys. Rev. Lett, 2005, 95(16):160501–4.
76 B. Wang, L. M. Duan. Engineering Superpositions of Coherence States in Co-herent Optical Pulses Through Cavity-assisted Interaction[J]. Phys. Rev. A, 2005,72(2):022320–5.
77 Z. J. Deng, M. Feng, K. L. Gao. Preparation of Entangled States of Four RemoteQubits in Decoherence-free Subspace[J]. Phys. Rev. A, 2007, 75(2):024302–4.
78 G. W. Lin, X. M. Lin, L. B. Chen, et al. Generation of Multiple-partite Cluster Statevia Cavity Qed[J]. Chin. Phys. B, 2008, 17(1):64–69.
79 X. H. Huang, X. M. Lin, G. W. Lin, et al. Generation of Atomic Greenberger-horne-zeilinger States and Cluster States Through Cavity-assisted Interaction[J].Chin. Phys. B, 2008, 17(12):4382–4387.
80 G. P. Guo, H. Zhang, T. Tu, et al. One-step Preparation of Cluster States inQuantum-dot Molecules[J]. Phys. Rev. A, 2007, 75(5):050301(R)–4.
81 A. Mitra, R. Vyas. Generation and Evolution of Entanglement in Coupled Quan-tum Dots Interacting with a Quantized Cavity Field[J]. Phys. Rev. A, 2007,76(5):052317–7.
82 F. Bodoky, M. Blaauboer. Production of Multipartite Entanglement for ElectronSpins in Quantum Dots[J]. Phys. Rev. A, 2007, 76(5):052309–8.
83 L. D. Contreras-Pulido, F. Rojas. Dynamic Generation of Bell States in a Double-quantum-dot Array Including Electron-photon Interaction[J]. Phys. Rev. A, 2008,77(3):032301–10.
84 J. Busch, E. S. Kyoseva, M. Trupke, et al. Entangling Distant Quantum Dots UsingClassical Interference[J]. Phys. Rev. A, 2008, 78(4):040301(R)–4.
85 Z. R. Lin, G. P. Guo, T. Tu, et al. Generation of Quantum-dot Cluster Stateswith a Superconducting Transmission Line Resonator[J]. Phys. Rev. Lett, 2008,101(23):230501–4.
86 R. Rossignoli, C. T. Schmiegelow. Entanglement Generation Resonances in ????Chains[J]. Phys. Rev. A, 2007, 75(1):012320–9.
87 N. Canosa, R. Rossignoli. Entanglement between Distant Qubits in Cyclic ????Chains[J]. Phys. Rev. A, 2007, 75(3):032350–8.
88 F. Galve, D. Zueco, S. Kohler, et al. Entanglement Resonance in Driven SpinChains[J]. Phys. Rev. A, 2009, 79(3):032332–5.
89 A. Muller, W. Fang, J. Lawall, et al. Creating Polarization-entangled Photon Pairsfrom a Semiconductor Quantum Dot Using the Optical Stark Effect[J]. Phys. Rev.Lett., 2009, 103(21):217402–4.
90 K. Yuasa, D. Burgarth, V. Giovannetti, et al. Efficient Generation of a MaximallyEntangled State by Repeated On- and Off-resonant Scattering of Ancilla Qubits[J].New J. Phys., 2010, 11(12):123027–19.
91 C. L. Ding, X. Y. Hao, J. H. Li, et al. Efficient Generation of Maximally EntangledStates via Four-wave Mixing in a Semiconductor Quantum-dot Nanostructure[J].Phys. Lett. A, 2010, 374(4):680–686.
92 A. Mohan, M. Felici, P. Gallo, et al. Polarization-entangled Photons Produced withHigh-symmetry Site-controlled Quantum Dots[J]. Nature Photon., 2010, 4:302–306.
93 F. Ciccarello, M. Paternostro, S. Bose, et al. Physical Model for the Generationof Ideal Resources in Multipartite Quantum Networking[J]. Phys. Rev. A, 2010,82(3):030302(R)–4.
94 M. Neeley, R. C. Bialczak, M. Lenander, et al. Generation of Three-qubit EntangledStates Using Superconducting Phase Qubits[J]. Nature, 2010, 467(7315):570–573.
95 L. DiCarlo, M. D. Reed, L. Sun, et al. Generation of Three-qubit Entangled StatesUsing Superconducting Phase Qubits[J]. Nature, 2010, 467(7315):574–578.
96 A. Einstein, B. Podolsky, N. Rosen. Can Quantum-mechnical Description of Phys-ical Reality Be Considered Complete?[J]. Phys. Rev., 1935, 47(10):777–780.
97 E. Schro¨dinger. Die Gegenwa¨rtige Situation in Der Quantenmechanik[J]. Natur-wissenschaften, 1935, 23(49):823–828.
98 C. Monroe, D. M. Meekhof, B. E. King, et al. A“Schro¨dinger Cat”SuperpositionState of an Atom[J]. Science, 1996, 272(5265):1131–1136.
99 J. S. Bell. On the Einstein-podolsky-rosen Paradox[J]. Physics, 1964, 1(3):195–200.
100 J. F. Clauser, M. A. Horne, A. Shimony, et al. Proposed Experiment to Test LocalHidden-variable Theories[J]. Phys. Rev. Lett., 1969, 23(15):880–884.
101 A. Aspect, P. Grangier, G. Roger. Experimental Realization of Einstein-podolsky-rosen-bohr Experiment[J]. Phys. Rev. Lett., 1982, 49(2):91–94.
102 D. M. Greenberger, M. A. Horne, A. Zeilinger. Going Beyond Bell’s Theorem,in Bell’s Theorem , Quantum Theory, and Conceptions of the Universe, Edited byM.kafatos[M]. Dordrecht, The Netherlands: Kluwer Academic, 1989:69–72.
103 D. M. Greenberger, M. A. Horne, A. Shinony, et al. Bell’s Theorem without In-equalities[J]. Am. J. Phys., 1990, 58(12):1131–1143.
104 W. Du¨r, G. Vidal, J. I. Cirac. Three Qubits Can Be Entangled in Two InequivalentWays[J]. Phys. Rev. A, 2000, 62(6):062314–12.
105朱红波,曾谨言.多粒子自旋纠缠态的构成与旋称[J].中国科学A辑, 2001,31(6):545–553.
106 F. Verstaete, J. Dehaene, B. D. Moor, et al. Four Qubits Can Be Entangled in NineDifferent Ways[J]. Phys. Rev. A, 2002, 65(5):052112–5.
107 J. Eisert, H. J. Briegel. Schmidt Measure as a Tool for Quantifying MultiparticleEntanglement[J]. Phys. Rev. A, 2001, 64(2):022306–4.
108 A. Peres. Separability Criterion for Density Matrices[J]. Phys. Rev. Lett, 1996,77(8):1413–1415.
109 M. Horodecki, P. Horodecki, R. Horodecki. Separability of Mixed States: Neces-sary and Sufficient Conditions[J]. Phys. Lett. A, 1996, 223(1-2):1–8.
110 P. Horodecki. Separability Criterion and Inseparable Mixed States with PositionPartial Transposition[J]. Phys. Lett. A, 1997, 232(5):333–339.
111 L. M. Duan, G. Giedke, J. I. Cirac, et al. Inseparability Criterion for ContinuousVariable System[J]. Phys. Rev. Lett., 2000, 84(12):2722–2725.
112 O. Rudolph. Further Results on the Cross Norm Criterion for Separability[J]. Quan.Inf. Proc., 2005, 4(3):219–239.
113 K. Chen, L. Wu. A Matrix Realign Method for Recognizing Entanglement[J].Quan. Inf. Compu., 2003, 3(3):193–202.
114 M. Horodecki, P. Horodecki, R. Horodecki. Separability of Mixed Quantum States:Linear Contractions and Permutation Criteria[J]. Open Syst. Inf. Dyn., 2006,13(1):103–111.
115 V. Vedral, M. B. Plenio, M. A. Rippin, et al. Quantifying Entanglement[J]. Phys.Rev. Lett., 1997, 78(12):2275–2279.
116 C. H. Bennett, H. J. Bernstein, S. Popescu, et al. Concentrating Partial Entangle-ment by Local Operation[J]. Phys. Rev. A, 1996, 53(4):2046–2052.
117 S. Hill, W. K. Wootters. Entanglement of a Pair of Quantum Bits[J]. Phys. Rev.Lett., 1997, 78(26):5022–5025.
118 W. K. Wootters. Entanglement of Formation of an Arbitrary State of Two Qubits[J].Phys. Rev. Lett., 1998, 80(10):2245–2248.
119 T. Yu, J. H. Eberly. Sudden Death of Entanglement: Classical Noise Effects[J].Opt. Commu., 2006, 264(2):393–397.
120 G. Vidal, R. F. Werner. Computable Measure of Entanglement[J]. Phys. Rev. A,2002, 65(3):032314–3.
121 T. Yu, J. H. Eberly. Finite-time Disentanglement via Spontaneous Emission[J].Phys. Rev. Lett., 2004, 93(14):140404–4.
122 M. Yo¨nac, T. Yu, J. H. Eberly. Sudden Death of Entanglement of Two Jaynes-cummings Atoms[J]. J. Phys. B: At. Mol. Opt. Phys., 2006, 39(15):S621–S625.
123 X. H. Gao, S. M. Fei, K. Wu. Lower Bounds of Concurrence for Tripartite QuantumSystem[J]. Phys. Rev. A, 2006, 74(5):050303(R)–4.
124 Z. J. Li, J. Q. Li, Y. H. Jin, et al. Time Evolution and Transfer of Entanglementbetween an Isolated Atom and a Jaynes-cummings Atom[J]. J. Phys. B: At. Mol.Opt. Phys., 2007, 40(17):3401–3411.
125 M. Yo¨nac, T. Yu, J. H. Eberly. Pairwise Concurrence Dynamics: A Four-qubitModel[J]. J. Phys. B: At. Mol. Opt. Phys., 2007, 40(9):S45–S59.
126 F. Mintert. Concurrence via Entanglement Witnesses[J]. Phys. Rev. A, 2007,75(5):052302–4.
127 M. Ikram, F. L. Li, M. S. Zubairy. Disentanglement in a Two-qubit System Sub-jected to Dissipation Environments[J]. Phys. Rev. A, 2007, 75(6):062336–9.
128 J. Niset, N. J. Cerf. Tight Bounds on the Concurrence of Quantum Superposition[J].Phys. Rev. A, 2007, 76(4):042328–7.
129 A. A. Qasimi, D. F. V. James. Sudden Death of Entanglement at Finite Tempera-ture[J]. Phys. Rev. A, 2008, 77(1):012117–4.
130 X. J. Ren, Z. W. Zhou, X. X. Zhou, et al. Proof of a Lower Bound for BipartiteConcurrence via Equivalence to an Observable Entanglement Measure[J]. Phys.Rev. A, 2008, 77(5):054302–2.
131 L. Aolita, R. Chaves, D. Cavalcanti, et al. Scaling Laws for the Decay of MultiqubitEntanglement[J]. Phys. Rev. Lett., 2008, 100(8):080501–4.
132 A. Salles, F. de Melo, M. P. Almeida, et al. Experimental Investigation of the Dy-namics of Entanglement: Sudden Death, Complementarity, and Continuous Moni-toring of the Environment[J]. Phys. Rev. A, 2008, 78(2):022322–15.
133 T. Yu, J. H. Eberly. Sudden Death of Entanglement[J]. Science, 2009,323(5914):598–601.
134 L. Mazzola, S. Maniscalco, J. Piilo, et al. Sudden Death and Sudden Birth of Entan-glement in Common Structured Reservoirs[J]. Phys. Rev. A, 2009, 79(4):042302–4.
135 L. Chen, X. Q. Shao, S. Zhang. Sudden Death and Sudden Birth of Entanglementin Common Structured Reservoirs[J]. Chin. Phys. B, 2009, 18(3):888–893.
136 X. J. Deng, M. F. Fang, G. D. Kang. Sudden Death and Sudden Birth of Entan-glement in Common Structured Reservoirs[J]. Chin. Phys. B, 2009, 18(10):4100–4104.
137 L. Chen, X. Q. Shao, S. Zhang. Sudden Death and Sudden Birth of Entanglementin Common Structured Reservoirs[J]. Chin. Phys. B, 2009, 18(11):4676–4682.
138 Y. J. Zhang, Z. X. Man, Y. J. Xia. Atomic Entanglement Sudden Death in a StronglyDriven Cavity Qed System[J]. J. Phys. B: At. Mol. Opt. Phys., 2009, 42(9):095503–7.
139 W. B. Cardoso, A. T. Avelar, B. Baseia, et al. Entanglement Sudden Death viaTwo-photon Processes in Cavity Qed[J]. J. Phys. B: At. Mol. Opt. Phys., 2009,42(19):095507–5.
140 M. P. Almeida, F. de Melo, M. Hor-Meyll, et al. Environment-induced SuddenDeath of Entanglement[J]. Science, 2007, 316(5824):579–582.
141 J. Laurat, K. S. Choi, H. Deng, et al. Heralded Entanglement between AtomicEnsembles: Preparation, Decoherence, and Scaling[J]. Phys. Rew. Lett., 2007,99(18):180504–4.
142 O. J. Far′?as, C. L. Latune, S. P. Walborn, et al. Determining the Dynamics ofEntanglement[J]. Science, 2009, 324(5933):1414–1417.
143 J. C. Wang, J. L. Jing. Quantum Decoherence in Noninertial Frames[J]. Phys. Rev.A, 2010, 82(3):032324–5.
144 H. Heydarl. Concurrence for General Multipartite States[J]. J. Phys. A: Math. Gen.,2006, 39(49):15225–15229.
145 L. Aolita. Measuring Multipartite Concurrence with a Single Factorization Observ-able[J]. Phys. Rev. Lett., 2006, 97(5):050501–4.
146 C. S. Yu, X. X. Yi, K. S. Song. Concurrence of Superposition[J]. Phys. Rev. A,2007, 75(2):022332–5.
147 A. Thilagam. Dynamics of a Multipartite System Undergoing Matter-state-photonConversion[J]. J. Phys. A: Math. Theor., 2009, 42(33):335301–13.
148 G. P. Guo, C. F. Li, J. Li, et al. Scheme for the Preparation of Multiparticle Entan-glement in Cavity Qed[J]. Phys. Rev. A, 2002, 65(4):042102–4.
149 S. B. Zheng. Generation of Greenberger-horne-zeilinger Sates for Three AtomsTrapped in a Cavity Beyond the Strong-coupling Regime[J]. Phys. Lett. A, 2008,372(5):591–595.
150 M. Hennrich, T. Legero, A. Kuhn, et al. Vacuum-stimulated Raman ScatteringBased on Adiabatic Passage in a High-finesse Optical Cavity[J]. Phys. Rev. Lett,2000, 85(23):4872–4875.
151 C. Wu, Y. Yeo, L. C. Kwek, et al. Quantum Nonlocally of Four-qubit EntnagledStates[J]. Phys. Rev. A, 2007, 75(3):032332–6.
152 P. G. Kwiat, A. J. Berglund, J. B. Altepeter, et al. Experimental Verification ofDecoherence-free Subspaces[J]. Science, 2000, 290(5491):498–501.
153 J. B. Alterpeter, P. G. Hadley, S. M. Wendelken, et al. Experimental Investi-gation of a Two-qubit Decoherence-free Subspace[J]. Phys. Rev. Lett., 2004,92(14):147901–4.
154 D. Kielpinski, V. Meyer, M. A. Rowe, et al. A Decoherence-free Quantum MemoryUsing Trapped Ions[J]. Science, 2001, 291(5506):1013–1015.
155 E. M. Fortunato, L. Viola, J. Hodges, et al. Implementation of Universal Controlon a Decoherence-free Qubit[J]. New J. Phys., 2002, 4(5):5.1–5.20.
156 J. E. Ollerenshaw, D. A. Lidar, L. E. Kay. Magnetic Resonance Realiza-tion of Decoherence-free Quantum Computation[J]. Phys. Rev. Lett., 2003,91(21):217904–4.
157 M. Bourennane, M. Eibl, S. Gaertner, et al. Decoherence-free Quantum Infor-mation Processing with Four-photon Entangled States[J]. Phys. Rev. Lett., 2004,92(10):107901–4.
158 D. Bouwmeester, J. W. Pan, M. Daniell, et al. Observation of Three-photonGreenberger-horne-zeilinger Entanglement[J]. Phys. Rev. Lett., 1999, 82(7):1345–1349.
159 W. Dur, H. Aschauer, H. J. Briegel. Multiparticle Entanglement Purification forGraph States[J]. Phys. Rev. Lett., 2003, 91(10):107903–4.
160 R. Raussendor, D. E. Browne, H. J. Briegel. Multiparticle Entanglement Purifica-tion for Graph States[J]. Phys. Rev. A, 2003, 68(2):022312–32.
161 M. Hein, J. Eisert, H. J. Briegel. Multiparticle Entanglement in Graph States[J].Phys. Rev. A, 2004, 69(6):062311–20.
162 M. Hein, W. Du¨o, J. Eisert, et al. Entanglement in Graph States and its Applica-tions[J]. quantum-ph, 2006:0602096–99.
163 M. V. D. Nest, J. Dehaene, B. D. Briegel. Graphical Description of the Ac-tion of Local Clifford Transformations on Graph States[J]. Phys. Rev. A, 2004,69(2):022316–7.
164 R. Raussendorf, H. J. Briegel. A One-way Quantum Computer[J]. Phys. Rev. Lett.,2001, 86(22):5188–5191.
165 A. Cabello, A. J. Lo′pez-Tarrida, P. Moreno, et al. Compact Set of Invariants Charac-terizing Graph States of up to Eight Qubits[J]. Phys. Rev. A, 2009, 80(1):012102–7.
166 A. Cabello, A. J. Lo′pez-Tarrida, P. Moreno, et al. Entanglement in Eight-qubitGraph States[J]. Phys. Lett. A, 2009, 337(26):2219–2225.
167 T. Tanamoto, Y. X. Liu, X. D. Hu, et al. Efficient Quantum Circuits for One-wayQuantum Computing[J]. Phys. Rev. Lett., 2009, 102(10):100501–4.
168 J. E. Mooij, T. P. Orlando, L. Levitov, et al. Josephson Persistent-current Qubit[J].Science, 1999, 285(5430):1036–1039.
169 Y. A. Pashkin, T. Yamamoto, O. Astafiev, et al. Quantum Oscillations in Two Cou-pled Charge Qubits[J]. Nature, 2003, 421(6925):823–826.
170 I. Chiorescu, Y. Nakamura, C. J. P. M. Harmans, et al. Coherent Quantum Dynamicsof a Superconducting Flux Qubit[J]. Science, 2003, 299(5614):1869–1871.
171 D. Loss, D. P. DiVincenzo. Quantum Computation with Quantum Dots[J]. Phys.Rev. A, 1998, 57(1):120–126.
172 W. G. van der Wiel, S. D. Franceschi, J. M. Elzeman, et al. Electron TransportThrough Double Quantum Dots[J]. Rev. Mod. Phys., 2003, 75(1):1–22.
173 N. Schuch, J. Siewert. Natural Two-qubit Gate for Quantum Computation Usingthe Xy Interaction[J]. Phys. Rev. A, 2003, 67(3):032301–8.
174 T. Tanamoto, K. Maruyama, Y. X. Liu, et al. Eifficient Purification Protocols UsingIswap Gates in Solid-state Qubits[J]. Phys. Rev. A, 2008, 78(6):062313–10.
2 P. Benioff. The Computer as a Physical System: A Microscopic Quantum Mechan-ical Hamlitonian Model of Computers as Represented by Turing Machines[J]. J.Stat. Phys., 1980, 22(5):563–591.
3 R. P. Feynman. Simulating Physics with Computers[J]. Int. J. Theor. Phys, 1982,21(6):467–488.
4 W. K. Wootters, W. H. Zurek. A Single Quantum Cannot Be Cloned[J]. Nature,1992, 299(5886):802–803.
5 M. A. Nielsen, I. L. Chuang. Quantum Computation and Quantum Information[M].
276 ed., Cambridge: Cambridge University Press, 2000:171–276.
6杨涛,潘建伟.量子信息技术的新进展[J].中国科学院院刊, 2004, 19(5):355–357.
7张国锋.量子纠缠的若干问题研究[D].山西:山西大学, 2004:6–9.
8 C. H. Bennett, F. Bessette, G. Brassard, et al. Experimental Quantum Cryptogra-phy[J]. J. Cryptology, 1992, 5(1):3–28.
9 J. Kempe. Approaches to Quantum Error Correction[C]//Progress in MathematicalPhysics Series. Birhaeuser, 2006:85–123.
10 C. H. Bennett, G. Brassard, C. Crepeau, et al. Teleporting an Unknown QuantumState via Dual Classical and Einstein-podolsky-rosen Channels[J]. Phys. Rev. Lett.,1993, 70(13):1895–1899.
11 A. K. Ekert. Quantum Cryptography Based on Bell’s Theorem[J]. Phys. Rev. Lett,1991, 67(6):661–663.
12 A. Steane. Quantum Computing[J]. Rep. Prog. Phys., 1998, 61(2):117–173.
13 K. Mattle, H. Weinfurter, P. G. Kwiat, et al. Dense Coding in Experimental Quan-tum Communication[J]. Phys. Rev. Lett., 1996, 79(25):4656–4659.
14 P. W. Shor. Algorithms for Quantum Computations: Discrete Logarithms and Fac-toring[C]//Proc. 35th Annu. Sym. Found. Comput. Science. Los Alamitos: IEEEComputer Society Press, 1994:124–134.
15 A. Ekert, R. Jozsa. Quantum Computation and Shor’s Factoring Algorithm[J]. Pev.Mod. Phys., 1996, 68(3):733–753.
16 L. K. Grover. Quantum Mechanics Helps in Searching for a Needle in aHaystack[J]. Phys. Rev. Lett, 1997, 79(2):325–328.
17 G. Rigolin. Quantum Teleportation of an Arbitrary Two-qubit State and its Relationto Multipartite Entanglement[J]. Phys. Rev. A, 2005, 71:032303–5.
18 S. B. Zheng, G. C. Guo. Scheme for Atomic-state Teleportation between Two BadCavities[J]. Phys. Rev. A, 2006, 73(3):032329–5.
19 Y. Yeo, W. K. Chua. Teleportation and Dense Coding with Genuine MultipartiteEntanglement[J]. Phys. Rev. Lett., 2006, 96(6):060502–4.
20 G. Gordon, G. Rigolin. Generalized Teleportation Protocol[J]. Phys. Rev. A, 2006,73(4):042309–4.
21 S. B. Zheng. State-independent Teleportation of an Atomic State between TwoCavities[J]. Phys. Rev. A, 2008, 77(4):044303–4.
22 D. Bouwmeester, J. W. Pan, K. Mattle, et al. Experimental Quantum Teleporta-tion[J]. Nature(London), 1997, 390(6660):575–579.
23 M. A. Nielsen, E. Knill, R. La?amme. Complete Quantum Teleportation UsingNuclear Magnetic Resonance[J]. Nature, 1998, 396(6706):52–55.
24 J. W. Pan, M. Daniell, S. Gasparoni, et al. Experimental Demonstration of Four-photon Entanglement and High-fidelity Teleportation[J]. Phys. Rev. Lett., 2001,86(20):4435–4438.
25 Z. Zhao, A. Y. Chen, A. N. Zhang, et al. Experimental Demonstration ofFive-photon Entanglement and Open-destination Teleportation[J]. Nature, 2004,430(6995):54–58.
26 Q. Zhang, A. Goebel, C. Wagenknecht, et al. Experimental Quantum Teleportationof a Two-qubit Composite System[J]. Nature Phys., 2006, 2(10):678–682.
27 Y. A. Chen, S. Chen, Z. S. Yuan, et al. Memory-built-in Quantum Teleportationwith Photonic and Atomic Qubits[J]. Nature Phys., 2008, 4(2):103–107.
28 S. Olmschenk, D. N. Matsukevich, P. Maunz, et al. Quantum Teleportation betweenDistant Matter Qubits[J]. Science, 2009, 323(5913):486–489.
29 X. M. Jin, J. G. Ren, B. Yang, et al. Experimental Free-space Quantum Teleporta-tion[J]. Nature Photon., 2010, 4(6):376–380.
30 C. H. Bennett, S. J. Wiesner. Communication via One and Two-particle Operatorson Einstein-podolsky-rosen States[J]. Phys. Rev. Lett., 1992, 69(20):2881–2884.
31 X. M. Fang, X. W. Zhu, M. Feng, et al. Experimental Implementation of DenseCoding Using Nuclear Magnetic Resonance[J]. Phys. Rev. A, 2000, 61(2):022307–5.
32 J. Zhang, K. Peng. Quantum Teleportation and Dense Coding by Means of BrightAmplitude-squeezed Light and Direct Measurement of a Bell State[J]. Phys. Rev.A, 2000, 62(6):064302–4.
33 J. C. Hao, C. F. Li, G. C. Guo. Controlled Dense Coding Using the Greenberger-horne-zeilinger State[J]. Phys. Rev. A, 2001, 63(5):054301–3.
34 X. S. Liu, G. L. Long, D. M. Tong, et al. General Scheme for Superdense Codingbetween Miltiparties[J]. Phys. Rev. A, 2002, 65(2):022304–4.
35 L. Ye, L. B. Yu. Scheme for Implementing Quantum Dense Coding Using TripartiteEntanglement in Cavity Qed[J]. Phys. Lett. A, 2005, 346(5-6):330–336.
36 S. Mozes, J. Oppenheim, B. Reznik. Deterministic Dense Coding with PartiallyEntangled States[J]. Phys. Rev. A, 2005, 71(1):012311–7.
37 G. M. Wang, M. S. Ying. Deterministic Distributed Dense Coding with StabilizerStates[J]. Phys. Rev. A, 2008, 77(3):032306–10.
38 C. H. Bennett, G. Brassard. Quantum Cryptography: Public Key Distribution andCoin Tossing[C]//Proceedings of IEEE International Conference on Computers,Systems and Signal Processing. Bangalore India, 1984:175–179.
39 K. Horodecki, D. Leung, H. K. Lo, et al. Quantum Key Distribution Based on Arbi-trarily Weak Distillable Entangled States[J]. Phys. Rev. Lett., 2006, 96(7):070501–4.
40 X. F. Ma, C. H. F. Fung, H. K. Lo. Quantum Key Distribution with EntangledPhoton Sources[J]. Phys. Rev. A, 2007, 76(1):012307–10.
41 A. Ling, M. P. Peloso, I. Marcikic, et al. Experimental Quantum Key DistributionBased on a Bell Test[J]. Phys. Rev. A, 2008, 78(2):020301(R)–4.
42 S. J. D. Phoenix, S. M. Barnett. Non-local Interatomic Correlations in the Micro-master[J]. J. Mod. Opt., 1993, 40(6):979–983.
43 I. K. Kudryavtsev, P. L. Knight. Atomic Entanglement and Bell’s Inequality[J]. J.Mod. Opt., 1993, 40(9):1673–1679.
44 J. I. Cirac, P. Zoller. Preparation of Macroscopic Superpositions in Many-atomSystems[J]. Phys. Rev. A, 1994, 50(4):R2799–R2802.
45 E. Haglay, X. Ma??tre, G. Nogues, et al. Generation of Einstein-podolsky-rosen Pairsof Atoms[J]. Phys. Rev. Lett., 1997, 79(1):1–5.
46 S. B. Zheng, G. C. Guo. Efficient Scheme for Two-atom Entanglement and Quan-tum Information Processing in Cavity Qed[J]. Phys. Rev. Lett., 2000, 85(11):2392–2395.
47 S. Osnaghi, P. Bertet, A. Auffeves, et al. Coherent Control of an Atomic Collisionin a Cavity[J]. Phys. Rev. Lett., 2001, 87(3):037902–4.
48 L. Ye, L. B. Yu, G. C. Guo. Generation of Entangled States in Cavity Qed[J]. Phys.Rev. A, 2005, 72(3):034304–4.
49 Y. F. Xiao, X. B. Zou, G. C. Guo. Generation of Atomic Entangled States withSelective Resonant Interaction in Cavity Quantum Electrodynamics[J]. Phys. Rev.A, 2007, 75(1):012310–5.
50 S. B. Li. Generation of Maximally Entangled Mixed States of Two Atomsvia On-resonance Asymmetric Atom-cavity Couplings[J]. Phys. Rev. A, 2007,75(5):054304–4.
51 P. J. D. Reis, S. S. Sharma. Generation of Field-mediated Three-qubit EntangledState Shared by Alice and Bob[J]. Phys. Rev. A, 2009, 79(1):012326–9.
52 J. I. Cirac, P. Zoller. Quantum Computations with Cold Trapped Ions[J]. Phys. Rev.Lett., 1995, 74(20):4091–4094.
53 A. S. Parkins, H. J. Kimble. Quantum State Transfer between Motion and Light[J].J. Opt. B:Quantum Semiclassical Opt., 1999, 1(4):496–504.
54 A. S. Parkins, E. larsabal. Preparation and Light-mediated Distribution of MotionalState Entanglement[J]. Phys. Rev. A, 2000, 63(1):012304–17.
55 A. Peng, A. S. Parkins. Motion-light Parametric Amplifier and Entanglement Dis-tributor[J]. Phys. Rev. A, 2002, 65(6):062323–8.
56 G. X. Li, H. T. Tan, S. P. Wu. Motional Entanglement for Two Trapped Ions inCascaded Optical[J]. Phys. Rev. A, 2004, 70(6):064301–4.
57 G. X. Li, S. P. Wu, G. M. Huang. Generation of Entanglement and Squeezing in theSystem of Two Ions Trapped in a Cavity[J]. Phys. Rev. A, 2005, 71(6):063817–9.
58 G. X. Li, S. P. Wu. Effect of Vibrational Heating on the Entangled Fiald from anIon Trapped in a Bimodal Cavity[J]. Phys. Rev. A, 2005, 72(6):064304–4.
59 G. Morigi, J. Eschner, S. Mancini, et al. Entangled Light Pulses from Single ColdAtoms[J]. Phys. Rev. Lett., 2006, 96(2):023601–4.
60 S. B. Zheng. Generation of Entangled States of Multiple Trapped Ions in ThermalMotion[J]. Phys. Rev. A, 2004, 70(4):045804–3.
61 G. X. Li. Generation of Pure Multipartite Entangled Vibrational States for IonsTrapped in a Cavity[J]. Phys. Rev. A, 2006, 74(5):055801–4.
62 A. Retzker, E. Solano, B. Reznik. Tavis-cummings Model and Collective Multi-qubit Entanglement in Trapped Ions[J]. Phys. Rev. A, 2007, 75(2):022312–6.
63 I. E. Linington, N. V. Vitanov. Decoherence-free Preparation of Dicke Sates ofTrapped Ions by Collective Stimulated Raman Adiabatic Passage[J]. Phys. Rev. A,2008, 77(6):062327–14.
64 X. W. Wang, G. J. Yang. Generation and Discrimination of a Type of Four-partiteEntangled State[J]. Phys. Rev. A, 2008, 78(2):024301–4.
65孙利群,王佳,田芊,等.自发参量下转换双光子场应用研究进展[J].物理,2000, 29(12):727–731.
66 P. G. Kwiat, E. Waks, A. G. White, et al. Ultrabright Source of Polarization-entangled Photons[J]. Phys. Rev. A, 1999, 60(2):R773–R776.
67 J. W. Pan, D. Bouwmeester, M. Daniell, et al. Experimental Test of QuantumNonlocality in Three-photon Greenberger-horne-zeilinger Entanglement[J]. Na-ture, 2000, 403(6769):515–519.
68 X. B. Zou, J. Shu, G. C. Guo. Simple Scheme for Generating Four-photonPolarization-entangled Decoherence-free States Using Spontaneous ParametricDown-conversions[J]. Phys. Rev. A, 2006, 73(5):054301–4.
69 B. Liu, Z. Y. Ou. Engineering Multiphoton Entangled States by Quantum Interfer-ence[J]. Phys. Rev. A, 2006, 74(3):035802–3.
70 Y. X. Gong, X. B. Zou, X. L. Niu, et al. Generation of Arbitrary Foue-hoton Polarization-entangled Decoherence-free Sates[J]. Phys. Rev. A, 2008,77(4):042317–5.
71 C. Y. Lu, X. Q. Zhou, O. Gu¨hne, et al. Experimental Entanglement of Six Photonsin Gragh States[J]. Nature Phys., 2007, 3(2):91–95.
72 S. Y. Baek, Y. H. Kim. Generating Entangled States of Two Ququarts Using LinearOptical Elements[J]. Phys. Rev. A, 2007, 75(3):034309–4.
73 K. Lemr, J. Fiura′sˇek. Preparation of Entangled States of Two Photons in SeveralSpatiel Modes[J]. Phys. Rev. A, 2008, 77(2):023802–8.
74 B. Stefanie, C. Gunther, Z. Anton, et al. Heralded Generation of Entangled PhotonPairs[J]. Nature Photon., 2010, 4(8):553–556.
75 J. Cho, H. W. Lee. Generation of Atomic Cluster States Through the Cavity Input-output Process[J]. Phys. Rev. Lett, 2005, 95(16):160501–4.
76 B. Wang, L. M. Duan. Engineering Superpositions of Coherence States in Co-herent Optical Pulses Through Cavity-assisted Interaction[J]. Phys. Rev. A, 2005,72(2):022320–5.
77 Z. J. Deng, M. Feng, K. L. Gao. Preparation of Entangled States of Four RemoteQubits in Decoherence-free Subspace[J]. Phys. Rev. A, 2007, 75(2):024302–4.
78 G. W. Lin, X. M. Lin, L. B. Chen, et al. Generation of Multiple-partite Cluster Statevia Cavity Qed[J]. Chin. Phys. B, 2008, 17(1):64–69.
79 X. H. Huang, X. M. Lin, G. W. Lin, et al. Generation of Atomic Greenberger-horne-zeilinger States and Cluster States Through Cavity-assisted Interaction[J].Chin. Phys. B, 2008, 17(12):4382–4387.
80 G. P. Guo, H. Zhang, T. Tu, et al. One-step Preparation of Cluster States inQuantum-dot Molecules[J]. Phys. Rev. A, 2007, 75(5):050301(R)–4.
81 A. Mitra, R. Vyas. Generation and Evolution of Entanglement in Coupled Quan-tum Dots Interacting with a Quantized Cavity Field[J]. Phys. Rev. A, 2007,76(5):052317–7.
82 F. Bodoky, M. Blaauboer. Production of Multipartite Entanglement for ElectronSpins in Quantum Dots[J]. Phys. Rev. A, 2007, 76(5):052309–8.
83 L. D. Contreras-Pulido, F. Rojas. Dynamic Generation of Bell States in a Double-quantum-dot Array Including Electron-photon Interaction[J]. Phys. Rev. A, 2008,77(3):032301–10.
84 J. Busch, E. S. Kyoseva, M. Trupke, et al. Entangling Distant Quantum Dots UsingClassical Interference[J]. Phys. Rev. A, 2008, 78(4):040301(R)–4.
85 Z. R. Lin, G. P. Guo, T. Tu, et al. Generation of Quantum-dot Cluster Stateswith a Superconducting Transmission Line Resonator[J]. Phys. Rev. Lett, 2008,101(23):230501–4.
86 R. Rossignoli, C. T. Schmiegelow. Entanglement Generation Resonances in ????Chains[J]. Phys. Rev. A, 2007, 75(1):012320–9.
87 N. Canosa, R. Rossignoli. Entanglement between Distant Qubits in Cyclic ????Chains[J]. Phys. Rev. A, 2007, 75(3):032350–8.
88 F. Galve, D. Zueco, S. Kohler, et al. Entanglement Resonance in Driven SpinChains[J]. Phys. Rev. A, 2009, 79(3):032332–5.
89 A. Muller, W. Fang, J. Lawall, et al. Creating Polarization-entangled Photon Pairsfrom a Semiconductor Quantum Dot Using the Optical Stark Effect[J]. Phys. Rev.Lett., 2009, 103(21):217402–4.
90 K. Yuasa, D. Burgarth, V. Giovannetti, et al. Efficient Generation of a MaximallyEntangled State by Repeated On- and Off-resonant Scattering of Ancilla Qubits[J].New J. Phys., 2010, 11(12):123027–19.
91 C. L. Ding, X. Y. Hao, J. H. Li, et al. Efficient Generation of Maximally EntangledStates via Four-wave Mixing in a Semiconductor Quantum-dot Nanostructure[J].Phys. Lett. A, 2010, 374(4):680–686.
92 A. Mohan, M. Felici, P. Gallo, et al. Polarization-entangled Photons Produced withHigh-symmetry Site-controlled Quantum Dots[J]. Nature Photon., 2010, 4:302–306.
93 F. Ciccarello, M. Paternostro, S. Bose, et al. Physical Model for the Generationof Ideal Resources in Multipartite Quantum Networking[J]. Phys. Rev. A, 2010,82(3):030302(R)–4.
94 M. Neeley, R. C. Bialczak, M. Lenander, et al. Generation of Three-qubit EntangledStates Using Superconducting Phase Qubits[J]. Nature, 2010, 467(7315):570–573.
95 L. DiCarlo, M. D. Reed, L. Sun, et al. Generation of Three-qubit Entangled StatesUsing Superconducting Phase Qubits[J]. Nature, 2010, 467(7315):574–578.
96 A. Einstein, B. Podolsky, N. Rosen. Can Quantum-mechnical Description of Phys-ical Reality Be Considered Complete?[J]. Phys. Rev., 1935, 47(10):777–780.
97 E. Schro¨dinger. Die Gegenwa¨rtige Situation in Der Quantenmechanik[J]. Natur-wissenschaften, 1935, 23(49):823–828.
98 C. Monroe, D. M. Meekhof, B. E. King, et al. A“Schro¨dinger Cat”SuperpositionState of an Atom[J]. Science, 1996, 272(5265):1131–1136.
99 J. S. Bell. On the Einstein-podolsky-rosen Paradox[J]. Physics, 1964, 1(3):195–200.
100 J. F. Clauser, M. A. Horne, A. Shimony, et al. Proposed Experiment to Test LocalHidden-variable Theories[J]. Phys. Rev. Lett., 1969, 23(15):880–884.
101 A. Aspect, P. Grangier, G. Roger. Experimental Realization of Einstein-podolsky-rosen-bohr Experiment[J]. Phys. Rev. Lett., 1982, 49(2):91–94.
102 D. M. Greenberger, M. A. Horne, A. Zeilinger. Going Beyond Bell’s Theorem,in Bell’s Theorem , Quantum Theory, and Conceptions of the Universe, Edited byM.kafatos[M]. Dordrecht, The Netherlands: Kluwer Academic, 1989:69–72.
103 D. M. Greenberger, M. A. Horne, A. Shinony, et al. Bell’s Theorem without In-equalities[J]. Am. J. Phys., 1990, 58(12):1131–1143.
104 W. Du¨r, G. Vidal, J. I. Cirac. Three Qubits Can Be Entangled in Two InequivalentWays[J]. Phys. Rev. A, 2000, 62(6):062314–12.
105朱红波,曾谨言.多粒子自旋纠缠态的构成与旋称[J].中国科学A辑, 2001,31(6):545–553.
106 F. Verstaete, J. Dehaene, B. D. Moor, et al. Four Qubits Can Be Entangled in NineDifferent Ways[J]. Phys. Rev. A, 2002, 65(5):052112–5.
107 J. Eisert, H. J. Briegel. Schmidt Measure as a Tool for Quantifying MultiparticleEntanglement[J]. Phys. Rev. A, 2001, 64(2):022306–4.
108 A. Peres. Separability Criterion for Density Matrices[J]. Phys. Rev. Lett, 1996,77(8):1413–1415.
109 M. Horodecki, P. Horodecki, R. Horodecki. Separability of Mixed States: Neces-sary and Sufficient Conditions[J]. Phys. Lett. A, 1996, 223(1-2):1–8.
110 P. Horodecki. Separability Criterion and Inseparable Mixed States with PositionPartial Transposition[J]. Phys. Lett. A, 1997, 232(5):333–339.
111 L. M. Duan, G. Giedke, J. I. Cirac, et al. Inseparability Criterion for ContinuousVariable System[J]. Phys. Rev. Lett., 2000, 84(12):2722–2725.
112 O. Rudolph. Further Results on the Cross Norm Criterion for Separability[J]. Quan.Inf. Proc., 2005, 4(3):219–239.
113 K. Chen, L. Wu. A Matrix Realign Method for Recognizing Entanglement[J].Quan. Inf. Compu., 2003, 3(3):193–202.
114 M. Horodecki, P. Horodecki, R. Horodecki. Separability of Mixed Quantum States:Linear Contractions and Permutation Criteria[J]. Open Syst. Inf. Dyn., 2006,13(1):103–111.
115 V. Vedral, M. B. Plenio, M. A. Rippin, et al. Quantifying Entanglement[J]. Phys.Rev. Lett., 1997, 78(12):2275–2279.
116 C. H. Bennett, H. J. Bernstein, S. Popescu, et al. Concentrating Partial Entangle-ment by Local Operation[J]. Phys. Rev. A, 1996, 53(4):2046–2052.
117 S. Hill, W. K. Wootters. Entanglement of a Pair of Quantum Bits[J]. Phys. Rev.Lett., 1997, 78(26):5022–5025.
118 W. K. Wootters. Entanglement of Formation of an Arbitrary State of Two Qubits[J].Phys. Rev. Lett., 1998, 80(10):2245–2248.
119 T. Yu, J. H. Eberly. Sudden Death of Entanglement: Classical Noise Effects[J].Opt. Commu., 2006, 264(2):393–397.
120 G. Vidal, R. F. Werner. Computable Measure of Entanglement[J]. Phys. Rev. A,2002, 65(3):032314–3.
121 T. Yu, J. H. Eberly. Finite-time Disentanglement via Spontaneous Emission[J].Phys. Rev. Lett., 2004, 93(14):140404–4.
122 M. Yo¨nac, T. Yu, J. H. Eberly. Sudden Death of Entanglement of Two Jaynes-cummings Atoms[J]. J. Phys. B: At. Mol. Opt. Phys., 2006, 39(15):S621–S625.
123 X. H. Gao, S. M. Fei, K. Wu. Lower Bounds of Concurrence for Tripartite QuantumSystem[J]. Phys. Rev. A, 2006, 74(5):050303(R)–4.
124 Z. J. Li, J. Q. Li, Y. H. Jin, et al. Time Evolution and Transfer of Entanglementbetween an Isolated Atom and a Jaynes-cummings Atom[J]. J. Phys. B: At. Mol.Opt. Phys., 2007, 40(17):3401–3411.
125 M. Yo¨nac, T. Yu, J. H. Eberly. Pairwise Concurrence Dynamics: A Four-qubitModel[J]. J. Phys. B: At. Mol. Opt. Phys., 2007, 40(9):S45–S59.
126 F. Mintert. Concurrence via Entanglement Witnesses[J]. Phys. Rev. A, 2007,75(5):052302–4.
127 M. Ikram, F. L. Li, M. S. Zubairy. Disentanglement in a Two-qubit System Sub-jected to Dissipation Environments[J]. Phys. Rev. A, 2007, 75(6):062336–9.
128 J. Niset, N. J. Cerf. Tight Bounds on the Concurrence of Quantum Superposition[J].Phys. Rev. A, 2007, 76(4):042328–7.
129 A. A. Qasimi, D. F. V. James. Sudden Death of Entanglement at Finite Tempera-ture[J]. Phys. Rev. A, 2008, 77(1):012117–4.
130 X. J. Ren, Z. W. Zhou, X. X. Zhou, et al. Proof of a Lower Bound for BipartiteConcurrence via Equivalence to an Observable Entanglement Measure[J]. Phys.Rev. A, 2008, 77(5):054302–2.
131 L. Aolita, R. Chaves, D. Cavalcanti, et al. Scaling Laws for the Decay of MultiqubitEntanglement[J]. Phys. Rev. Lett., 2008, 100(8):080501–4.
132 A. Salles, F. de Melo, M. P. Almeida, et al. Experimental Investigation of the Dy-namics of Entanglement: Sudden Death, Complementarity, and Continuous Moni-toring of the Environment[J]. Phys. Rev. A, 2008, 78(2):022322–15.
133 T. Yu, J. H. Eberly. Sudden Death of Entanglement[J]. Science, 2009,323(5914):598–601.
134 L. Mazzola, S. Maniscalco, J. Piilo, et al. Sudden Death and Sudden Birth of Entan-glement in Common Structured Reservoirs[J]. Phys. Rev. A, 2009, 79(4):042302–4.
135 L. Chen, X. Q. Shao, S. Zhang. Sudden Death and Sudden Birth of Entanglementin Common Structured Reservoirs[J]. Chin. Phys. B, 2009, 18(3):888–893.
136 X. J. Deng, M. F. Fang, G. D. Kang. Sudden Death and Sudden Birth of Entan-glement in Common Structured Reservoirs[J]. Chin. Phys. B, 2009, 18(10):4100–4104.
137 L. Chen, X. Q. Shao, S. Zhang. Sudden Death and Sudden Birth of Entanglementin Common Structured Reservoirs[J]. Chin. Phys. B, 2009, 18(11):4676–4682.
138 Y. J. Zhang, Z. X. Man, Y. J. Xia. Atomic Entanglement Sudden Death in a StronglyDriven Cavity Qed System[J]. J. Phys. B: At. Mol. Opt. Phys., 2009, 42(9):095503–7.
139 W. B. Cardoso, A. T. Avelar, B. Baseia, et al. Entanglement Sudden Death viaTwo-photon Processes in Cavity Qed[J]. J. Phys. B: At. Mol. Opt. Phys., 2009,42(19):095507–5.
140 M. P. Almeida, F. de Melo, M. Hor-Meyll, et al. Environment-induced SuddenDeath of Entanglement[J]. Science, 2007, 316(5824):579–582.
141 J. Laurat, K. S. Choi, H. Deng, et al. Heralded Entanglement between AtomicEnsembles: Preparation, Decoherence, and Scaling[J]. Phys. Rew. Lett., 2007,99(18):180504–4.
142 O. J. Far′?as, C. L. Latune, S. P. Walborn, et al. Determining the Dynamics ofEntanglement[J]. Science, 2009, 324(5933):1414–1417.
143 J. C. Wang, J. L. Jing. Quantum Decoherence in Noninertial Frames[J]. Phys. Rev.A, 2010, 82(3):032324–5.
144 H. Heydarl. Concurrence for General Multipartite States[J]. J. Phys. A: Math. Gen.,2006, 39(49):15225–15229.
145 L. Aolita. Measuring Multipartite Concurrence with a Single Factorization Observ-able[J]. Phys. Rev. Lett., 2006, 97(5):050501–4.
146 C. S. Yu, X. X. Yi, K. S. Song. Concurrence of Superposition[J]. Phys. Rev. A,2007, 75(2):022332–5.
147 A. Thilagam. Dynamics of a Multipartite System Undergoing Matter-state-photonConversion[J]. J. Phys. A: Math. Theor., 2009, 42(33):335301–13.
148 G. P. Guo, C. F. Li, J. Li, et al. Scheme for the Preparation of Multiparticle Entan-glement in Cavity Qed[J]. Phys. Rev. A, 2002, 65(4):042102–4.
149 S. B. Zheng. Generation of Greenberger-horne-zeilinger Sates for Three AtomsTrapped in a Cavity Beyond the Strong-coupling Regime[J]. Phys. Lett. A, 2008,372(5):591–595.
150 M. Hennrich, T. Legero, A. Kuhn, et al. Vacuum-stimulated Raman ScatteringBased on Adiabatic Passage in a High-finesse Optical Cavity[J]. Phys. Rev. Lett,2000, 85(23):4872–4875.
151 C. Wu, Y. Yeo, L. C. Kwek, et al. Quantum Nonlocally of Four-qubit EntnagledStates[J]. Phys. Rev. A, 2007, 75(3):032332–6.
152 P. G. Kwiat, A. J. Berglund, J. B. Altepeter, et al. Experimental Verification ofDecoherence-free Subspaces[J]. Science, 2000, 290(5491):498–501.
153 J. B. Alterpeter, P. G. Hadley, S. M. Wendelken, et al. Experimental Investi-gation of a Two-qubit Decoherence-free Subspace[J]. Phys. Rev. Lett., 2004,92(14):147901–4.
154 D. Kielpinski, V. Meyer, M. A. Rowe, et al. A Decoherence-free Quantum MemoryUsing Trapped Ions[J]. Science, 2001, 291(5506):1013–1015.
155 E. M. Fortunato, L. Viola, J. Hodges, et al. Implementation of Universal Controlon a Decoherence-free Qubit[J]. New J. Phys., 2002, 4(5):5.1–5.20.
156 J. E. Ollerenshaw, D. A. Lidar, L. E. Kay. Magnetic Resonance Realiza-tion of Decoherence-free Quantum Computation[J]. Phys. Rev. Lett., 2003,91(21):217904–4.
157 M. Bourennane, M. Eibl, S. Gaertner, et al. Decoherence-free Quantum Infor-mation Processing with Four-photon Entangled States[J]. Phys. Rev. Lett., 2004,92(10):107901–4.
158 D. Bouwmeester, J. W. Pan, M. Daniell, et al. Observation of Three-photonGreenberger-horne-zeilinger Entanglement[J]. Phys. Rev. Lett., 1999, 82(7):1345–1349.
159 W. Dur, H. Aschauer, H. J. Briegel. Multiparticle Entanglement Purification forGraph States[J]. Phys. Rev. Lett., 2003, 91(10):107903–4.
160 R. Raussendor, D. E. Browne, H. J. Briegel. Multiparticle Entanglement Purifica-tion for Graph States[J]. Phys. Rev. A, 2003, 68(2):022312–32.
161 M. Hein, J. Eisert, H. J. Briegel. Multiparticle Entanglement in Graph States[J].Phys. Rev. A, 2004, 69(6):062311–20.
162 M. Hein, W. Du¨o, J. Eisert, et al. Entanglement in Graph States and its Applica-tions[J]. quantum-ph, 2006:0602096–99.
163 M. V. D. Nest, J. Dehaene, B. D. Briegel. Graphical Description of the Ac-tion of Local Clifford Transformations on Graph States[J]. Phys. Rev. A, 2004,69(2):022316–7.
164 R. Raussendorf, H. J. Briegel. A One-way Quantum Computer[J]. Phys. Rev. Lett.,2001, 86(22):5188–5191.
165 A. Cabello, A. J. Lo′pez-Tarrida, P. Moreno, et al. Compact Set of Invariants Charac-terizing Graph States of up to Eight Qubits[J]. Phys. Rev. A, 2009, 80(1):012102–7.
166 A. Cabello, A. J. Lo′pez-Tarrida, P. Moreno, et al. Entanglement in Eight-qubitGraph States[J]. Phys. Lett. A, 2009, 337(26):2219–2225.
167 T. Tanamoto, Y. X. Liu, X. D. Hu, et al. Efficient Quantum Circuits for One-wayQuantum Computing[J]. Phys. Rev. Lett., 2009, 102(10):100501–4.
168 J. E. Mooij, T. P. Orlando, L. Levitov, et al. Josephson Persistent-current Qubit[J].Science, 1999, 285(5430):1036–1039.
169 Y. A. Pashkin, T. Yamamoto, O. Astafiev, et al. Quantum Oscillations in Two Cou-pled Charge Qubits[J]. Nature, 2003, 421(6925):823–826.
170 I. Chiorescu, Y. Nakamura, C. J. P. M. Harmans, et al. Coherent Quantum Dynamicsof a Superconducting Flux Qubit[J]. Science, 2003, 299(5614):1869–1871.
171 D. Loss, D. P. DiVincenzo. Quantum Computation with Quantum Dots[J]. Phys.Rev. A, 1998, 57(1):120–126.
172 W. G. van der Wiel, S. D. Franceschi, J. M. Elzeman, et al. Electron TransportThrough Double Quantum Dots[J]. Rev. Mod. Phys., 2003, 75(1):1–22.
173 N. Schuch, J. Siewert. Natural Two-qubit Gate for Quantum Computation Usingthe Xy Interaction[J]. Phys. Rev. A, 2003, 67(3):032301–8.
174 T. Tanamoto, K. Maruyama, Y. X. Liu, et al. Eifficient Purification Protocols UsingIswap Gates in Solid-state Qubits[J]. Phys. Rev. A, 2008, 78(6):062313–10.