基于腔QED纠缠态的制备及应用
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摘要
量子信息学是量子力学与信息科学相结合,以研究信息处理为目的的学科。在信息处理的过程中,信息是以量子态为载体进行态演化的过程。所以,量子纠缠是量子信息学中非常重要的研究对象。量子态独特的性质是实现高保密量子通信的基础。腔量子电动力学(腔QED)是一种可以实现量子纠缠的物理体系,它具有非常好的前景。腔QED主要研究光子与原子在狭小的腔内,特定的边界条件下的相互作用。
量子纠缠态是量子通信中基本的物理资源。在量子信息的各方面,如量子隐形传态、量子密钥分配、量子计算等都起着重要作用。纠缠系统受到实验条件、环境噪声的影响,对纠缠产生消相干作用,使用这样的纠缠态进行量子通信将会导致信息失真。因此,在量子通信中,只有对纠缠态准确的识别,对纠缠态纯化才能保证量子态的可靠传送。如何实现纠缠态的准确识别和提高纠缠态的纯化是量子通信中的重要课题。
本论文的主要内容是基于腔QED的纠缠态制备及应用的理论研究。论文的主要工作涉及以下几个方面：
1.利用量子点和微腔的耦合系统来制备纠缠态。先分析了腔的反射和透射特性,我们利用光子与腔相互作用规律,利用非破坏性测量原理,制备纠缠态,包括Bell态和GHZ态,最后模拟仿真腔的反射和透射对纠缠态成功率的影响。在强耦合的条件下,纠缠态的成功几率接近于1。
2.在论文的第五章,简单的介绍了下纠缠的应用—量子密钥分配原理和量子远程传态的实现过程。在这章,还分析了一种纠缠态的纯化方法,利用入射光子进入系统后的变化规律,达到奇偶校验的效果,最终使用腔QED系统实现纠缠态的纯化。
Quantum information is a new subject in order to research the quantum information processing, which uses the basic principles of quantum mechanics in information science related field. Quantum entanglement is a very important research object in the quantum information. It is the foundation of realizing safety quantum communication. Cavity quantum electrodynamics (cavity QED) is one of physical system which can realize the quantum entanglement. Cavity QED research photon and atom in the narrow lumen, specific boundary conditions of the interaction.
Quantum entanglement is the basic physical resources in the quantum communication. In all aspects of quantum information, such as quantum recessive transmission, quantum key distribution and quantum computation and so on, it plays an important role in the related field. Entanglement system is experimental conditions, the influence of environmental noise, the entanglement produce away coherent function, use the entangled state in the quantum communication will lead to information distortion. Therefore, in quantum communication, need to accurately identify and entanglement of entanglement purification can guarantee the reliable transmission quantum state, how to realize the entangled state to identify and improve the entanglement purification is also an important subject of quantum communication. The main content of this paper is based on cavity QED entangled state of preparation and application of the theory research. The paper main work involved in the following aspects:
1. Use a new type of cavity preparation entangled state. The first analysis of the cavity of the reflection and transmission characteristics, and then in cavity QED system, we use the photon and cavity interaction rules, the use of nondestructive measurement principle, preparation of entangled state, including bell state and GHZ state, finally simulation chamber of the reflection and transmission to the influence of the success rate of entanglement. In the strong coupling conditions, entangled state success probability close to1.
2. In the fifth chapter of the paper, simply introduces the application of entanglement. In this chapter, a kind of entanglement purification methods, using the incident photon after entering system, achieve the effect of parity, finally using cavity QED system achieve entanglement purification.
量子纠缠态是量子通信中基本的物理资源。在量子信息的各方面,如量子隐形传态、量子密钥分配、量子计算等都起着重要作用。纠缠系统受到实验条件、环境噪声的影响,对纠缠产生消相干作用,使用这样的纠缠态进行量子通信将会导致信息失真。因此,在量子通信中,只有对纠缠态准确的识别,对纠缠态纯化才能保证量子态的可靠传送。如何实现纠缠态的准确识别和提高纠缠态的纯化是量子通信中的重要课题。
本论文的主要内容是基于腔QED的纠缠态制备及应用的理论研究。论文的主要工作涉及以下几个方面：
1.利用量子点和微腔的耦合系统来制备纠缠态。先分析了腔的反射和透射特性,我们利用光子与腔相互作用规律,利用非破坏性测量原理,制备纠缠态,包括Bell态和GHZ态,最后模拟仿真腔的反射和透射对纠缠态成功率的影响。在强耦合的条件下,纠缠态的成功几率接近于1。
2.在论文的第五章,简单的介绍了下纠缠的应用—量子密钥分配原理和量子远程传态的实现过程。在这章,还分析了一种纠缠态的纯化方法,利用入射光子进入系统后的变化规律,达到奇偶校验的效果,最终使用腔QED系统实现纠缠态的纯化。
Quantum information is a new subject in order to research the quantum information processing, which uses the basic principles of quantum mechanics in information science related field. Quantum entanglement is a very important research object in the quantum information. It is the foundation of realizing safety quantum communication. Cavity quantum electrodynamics (cavity QED) is one of physical system which can realize the quantum entanglement. Cavity QED research photon and atom in the narrow lumen, specific boundary conditions of the interaction.
Quantum entanglement is the basic physical resources in the quantum communication. In all aspects of quantum information, such as quantum recessive transmission, quantum key distribution and quantum computation and so on, it plays an important role in the related field. Entanglement system is experimental conditions, the influence of environmental noise, the entanglement produce away coherent function, use the entangled state in the quantum communication will lead to information distortion. Therefore, in quantum communication, need to accurately identify and entanglement of entanglement purification can guarantee the reliable transmission quantum state, how to realize the entangled state to identify and improve the entanglement purification is also an important subject of quantum communication. The main content of this paper is based on cavity QED entangled state of preparation and application of the theory research. The paper main work involved in the following aspects:
1. Use a new type of cavity preparation entangled state. The first analysis of the cavity of the reflection and transmission characteristics, and then in cavity QED system, we use the photon and cavity interaction rules, the use of nondestructive measurement principle, preparation of entangled state, including bell state and GHZ state, finally simulation chamber of the reflection and transmission to the influence of the success rate of entanglement. In the strong coupling conditions, entangled state success probability close to1.
2. In the fifth chapter of the paper, simply introduces the application of entanglement. In this chapter, a kind of entanglement purification methods, using the incident photon after entering system, achieve the effect of parity, finally using cavity QED system achieve entanglement purification.
引文
[1]Rivest R L, Shamir A, Adleman A. A method for obtaining digital signitures and public key cryptosystems. Communications of the ACM,21(2):120-126,1978
[2]Shannon C E. A Mathematical Theory of Commuication. Bell Systems Technical Journal,Vol.27 pp 379-423,623-656,1948
[3]曾贵华.量子密码学.科学出版社.2006.06
[4]Deutsch D Quantum theory, the Church-Turing principle and the universal quantum computer [J]. Proc R Soc A,1985,400:97～117
[5]Shor P W, Algorithms for quantum computation:Discrete logarithms and factoring[C], Proc of the 35th Annual Symp on Foundations of Computer Science. New Mexico:IEEE Computer Society Press.1997.124～134
[6]Grover L K, A fast quantum mechanical algorithm for database search [C], Proc of the 28th Annual ACM Symp on the Theory of Computing,1996,212～219; Grover L K, Quantum mechanics helps in searching of for a needle in a haystack, Phys. Rev. Lett.1997,79:325～328
[7]Tittel W, Weihs G. Photonic entanglement for fundamental test and quantum communication. Quantum Information and Computation,1:3-56,2001
[8]Yamamoto T, Pashkin Y A, Astafiev O et al. Demonstration of conditional gate operation using superconducting charge qubits [J], Nature,2003,425:941～944
[9]Pellizzari T, Gardiner S A, and Cirac J I et al. Decoherence, continuous observation, and quantum computing; A Cavity QED Model [J],1995. Phys. Rev. Lett.75,3788～3791
[10]Zheng S B, Guo G C, Efficient scheme for two-atom entanglement and quantum information processing in cavity QED [J]. Phys. Rev. Lett,200,85:2392
[11]Zheng S B, One-step synthesis of multiatom Greenberger-Horne-Zeilinger states [J], Phys. Rev. Lett,2001 87:230404
[12]Mabuchi H, Doherty A C, Cavity quantum electrodynamics:coherence in context [J]. Science,2002,298:1372
[13]Duan L M, Kuzmich A, Kimble H J, Cavity QED and quantum-information processing with "hot" trapped atoms [J]. Phys. Rev. A,2003,67:032305
[14]Pachos J K, Beige A., Decoherence-free dynamical and geometrical entangling phase gates [J]. Phys. Rev. A,2004,69:033817
[15]Cirac J I, Zoller P, Quantum computations with cold trapped ions[J], Phys. Rev. Lett.,1995,74:4091～4094
[16]Schmidt-Kaler F, Haffner H, Riebe M et al, Realization of the Cirac-Zoller controlled-NOT quantum gate[J], Nature,2003,422:408～411
[17]Gulde S, Riebe M, and Lancaster GP T et, al. Implementation of the Deutsch-Jozsa algorithm on an ion-trap quantum computer [J], Nature,2003 421: 48～50
[18]Christophe M, Townsend P D. Quantum key distribution over distances as long as 30km.Opt. Lett,20(16):1695,1995
[19]Stucki D, Gisin N, Guinnard O, et al. Quantum key distribution over 67km with a plug-play system. New. J. Phys,4:43,2002
[20]Buttler W T, Hughes R J, Lamoreaux S K, et al. Daylight quantum key distribution over 1.6km. Phys. Rev. Lett,84(24):5652-5655,2000
[21]Kurtsiefer C, Zarda P, Halder M, et al. A step towards global key distribution. Nature,419:450,2002
[22]Ursin R, Tiefenbacher F, Schmitt-Manderbach T, et al. Entanglement-based quantum communication over 144 km. Nature Physics,3:481-486,2007
[23]喀兴林.高等量子力学(第二版).北京：高等教育出版社,2001.8.
[24]Wootters W K, Zurek W H. A single quantum cannot be cloned. Nature, 299:802-803,1982
[25]Bell J S, On the Einstein-Podolsky-Rosen Paradox [J], Physics,1964,1:195～200
[26]Aspect A, Dalibard J and Roger G, Experimental Test of Bell's Inequalities Using Time-Varying Analyzers [J], Phys. Rev. Lett.1982,49:1804～1807
[27]Bohm D, Quantum Theory [M], Englewood Cliffs, NJ:Prentice Hall,1951. 614～823
[28]Greenberger D M, Home M A, Zeilinger A. In Bell's theorem, quantum theory and conceptions of the universe.1989
[29]Bell J S. On the Einstein-podolsky-rosen paradox. Physics(Long Island City,N.Y).1:195,1964
[30]Aspect A, Dalibard J, Roger G Experimental Test of Bell's Inequalities Using Time-Varying Analyzers. Phys.Rev.Lett.49:1804-1807,1982
[31]Beige A, Englert B G, Kurtsiefer C, et al. Secure communication with single-photon two qubit states. J. Phys. A:Math. Gen,35:L407-L413,2002
[32]Hu C Y, Munro W J, O'Brien J L, and Rarity J G. Proposed entanglement beam splitter using a quantum-dot spin in a double-sided optical microcavity, Phys. Rev. B.80:205326,2009
[33]Bennett C H, Brassard G and Crepeau C et al. Teleporting an Unknown Quantum State via Dual Classical and EPR Channels [J], Phys. Rev. Lett.1993, 70:1895～1899
[34]Beige A, Englert B G, Kurtsiefer C, et al. Secure communication with a publicly known key. Acta Phys. Pol. A,101(6):357,2002
[35]Bennett C H, Brassard G. Quantum cryptography:public key distribution and coin tossing.Proc. IEEE Int.Conf. on Computers, Systems and Signal Processing, Bangalore, India(IEEE, New York),175-179,1984
[36]Wang C, Zhang Y, and Jin G S. Entanglement purification and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities. Phys. Rev. A.84:032307,2011
[37]Deutsch D, Ekert A, Jozsa R, Macckiavello C, Popcscu S, Sanpera A. Quantum Privacy Amplification and the Security of Quantum Cryptography over Noisy Channels.Phys. Rev. Lett.77:2818,1996
[38]Sheng Y B, Deng F G,Zhou H Y. Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity. Phys. Rev. A.77:042308,2008
[39]Zhao Z, Yang T, Chen Y A, Zhang A N, Pan J W. Experimental Realization of Entanglement Concentration and a Quantum Repeater. Phys. Rev. Lett. 90:207901,2003
[40]Sheng Y B, Deng F G, Zhou H Y. Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics. Phys. Rev. A.77:062325,2008
[2]Shannon C E. A Mathematical Theory of Commuication. Bell Systems Technical Journal,Vol.27 pp 379-423,623-656,1948
[3]曾贵华.量子密码学.科学出版社.2006.06
[4]Deutsch D Quantum theory, the Church-Turing principle and the universal quantum computer [J]. Proc R Soc A,1985,400:97～117
[5]Shor P W, Algorithms for quantum computation:Discrete logarithms and factoring[C], Proc of the 35th Annual Symp on Foundations of Computer Science. New Mexico:IEEE Computer Society Press.1997.124～134
[6]Grover L K, A fast quantum mechanical algorithm for database search [C], Proc of the 28th Annual ACM Symp on the Theory of Computing,1996,212～219; Grover L K, Quantum mechanics helps in searching of for a needle in a haystack, Phys. Rev. Lett.1997,79:325～328
[7]Tittel W, Weihs G. Photonic entanglement for fundamental test and quantum communication. Quantum Information and Computation,1:3-56,2001
[8]Yamamoto T, Pashkin Y A, Astafiev O et al. Demonstration of conditional gate operation using superconducting charge qubits [J], Nature,2003,425:941～944
[9]Pellizzari T, Gardiner S A, and Cirac J I et al. Decoherence, continuous observation, and quantum computing; A Cavity QED Model [J],1995. Phys. Rev. Lett.75,3788～3791
[10]Zheng S B, Guo G C, Efficient scheme for two-atom entanglement and quantum information processing in cavity QED [J]. Phys. Rev. Lett,200,85:2392
[11]Zheng S B, One-step synthesis of multiatom Greenberger-Horne-Zeilinger states [J], Phys. Rev. Lett,2001 87:230404
[12]Mabuchi H, Doherty A C, Cavity quantum electrodynamics:coherence in context [J]. Science,2002,298:1372
[13]Duan L M, Kuzmich A, Kimble H J, Cavity QED and quantum-information processing with "hot" trapped atoms [J]. Phys. Rev. A,2003,67:032305
[14]Pachos J K, Beige A., Decoherence-free dynamical and geometrical entangling phase gates [J]. Phys. Rev. A,2004,69:033817
[15]Cirac J I, Zoller P, Quantum computations with cold trapped ions[J], Phys. Rev. Lett.,1995,74:4091～4094
[16]Schmidt-Kaler F, Haffner H, Riebe M et al, Realization of the Cirac-Zoller controlled-NOT quantum gate[J], Nature,2003,422:408～411
[17]Gulde S, Riebe M, and Lancaster GP T et, al. Implementation of the Deutsch-Jozsa algorithm on an ion-trap quantum computer [J], Nature,2003 421: 48～50
[18]Christophe M, Townsend P D. Quantum key distribution over distances as long as 30km.Opt. Lett,20(16):1695,1995
[19]Stucki D, Gisin N, Guinnard O, et al. Quantum key distribution over 67km with a plug-play system. New. J. Phys,4:43,2002
[20]Buttler W T, Hughes R J, Lamoreaux S K, et al. Daylight quantum key distribution over 1.6km. Phys. Rev. Lett,84(24):5652-5655,2000
[21]Kurtsiefer C, Zarda P, Halder M, et al. A step towards global key distribution. Nature,419:450,2002
[22]Ursin R, Tiefenbacher F, Schmitt-Manderbach T, et al. Entanglement-based quantum communication over 144 km. Nature Physics,3:481-486,2007
[23]喀兴林.高等量子力学(第二版).北京：高等教育出版社,2001.8.
[24]Wootters W K, Zurek W H. A single quantum cannot be cloned. Nature, 299:802-803,1982
[25]Bell J S, On the Einstein-Podolsky-Rosen Paradox [J], Physics,1964,1:195～200
[26]Aspect A, Dalibard J and Roger G, Experimental Test of Bell's Inequalities Using Time-Varying Analyzers [J], Phys. Rev. Lett.1982,49:1804～1807
[27]Bohm D, Quantum Theory [M], Englewood Cliffs, NJ:Prentice Hall,1951. 614～823
[28]Greenberger D M, Home M A, Zeilinger A. In Bell's theorem, quantum theory and conceptions of the universe.1989
[29]Bell J S. On the Einstein-podolsky-rosen paradox. Physics(Long Island City,N.Y).1:195,1964
[30]Aspect A, Dalibard J, Roger G Experimental Test of Bell's Inequalities Using Time-Varying Analyzers. Phys.Rev.Lett.49:1804-1807,1982
[31]Beige A, Englert B G, Kurtsiefer C, et al. Secure communication with single-photon two qubit states. J. Phys. A:Math. Gen,35:L407-L413,2002
[32]Hu C Y, Munro W J, O'Brien J L, and Rarity J G. Proposed entanglement beam splitter using a quantum-dot spin in a double-sided optical microcavity, Phys. Rev. B.80:205326,2009
[33]Bennett C H, Brassard G and Crepeau C et al. Teleporting an Unknown Quantum State via Dual Classical and EPR Channels [J], Phys. Rev. Lett.1993, 70:1895～1899
[34]Beige A, Englert B G, Kurtsiefer C, et al. Secure communication with a publicly known key. Acta Phys. Pol. A,101(6):357,2002
[35]Bennett C H, Brassard G. Quantum cryptography:public key distribution and coin tossing.Proc. IEEE Int.Conf. on Computers, Systems and Signal Processing, Bangalore, India(IEEE, New York),175-179,1984
[36]Wang C, Zhang Y, and Jin G S. Entanglement purification and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities. Phys. Rev. A.84:032307,2011
[37]Deutsch D, Ekert A, Jozsa R, Macckiavello C, Popcscu S, Sanpera A. Quantum Privacy Amplification and the Security of Quantum Cryptography over Noisy Channels.Phys. Rev. Lett.77:2818,1996
[38]Sheng Y B, Deng F G,Zhou H Y. Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity. Phys. Rev. A.77:042308,2008
[39]Zhao Z, Yang T, Chen Y A, Zhang A N, Pan J W. Experimental Realization of Entanglement Concentration and a Quantum Repeater. Phys. Rev. Lett. 90:207901,2003
[40]Sheng Y B, Deng F G, Zhou H Y. Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics. Phys. Rev. A.77:062325,2008