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宏观-微观纠缠最早起源于薛定谔的猫思想实验, 是指在宏观体系与微观体系之间建立量子纠缠. 实现宏观-微观纠缠可以利用多种物理体系来完成, 本文重点介绍了在光学体系中制备和检验宏观-微观纠缠的发展过程. 从最初的受激辐射单光子量子克隆到光学参量放大, 再到相空间的位移操作, 实验上制备宏观-微观纠缠的方法取得了长足的进步. 利用非线性光学参量放大过程制备的宏观-微观纠缠的光子数可以达到104量级, 人眼已经可以观察到, 因此使用人眼作为探测器来检验宏观-微观纠缠的实验开始出现. 但随后人们意识到, 粗精度的光子数探测器, 例如人眼, 无法严格判定宏观-微观纠缠的存在. 为了解决这个难题, 提出了一种巧妙的方法, 即在制备宏-微观纠缠后, 利用局域操作过程将宏观态再变为微观态, 通过判定微观纠缠存在的方法来判定宏微观纠缠的存在. 之后相空间的位移操作方法将宏观态的粒子数提高到108, 并且实现了纠缠的严格检验. 利用光机械实现宏观-微观纠缠的方案也被提出. 由于量子密钥分配中纠缠是必要条件, 而宏观-微观纠缠态光子数较多这一优势可能会对量子密钥分配的传输距离有所提高. 本文介绍了利用相位纠缠的相干态来进行量子秘钥分配的方案, 探讨了利用宏观-微观纠缠实现量子密钥分配的可能性.Macro-micro entanglement originates from the Schrodinger's Cat paradox. The paradox has been attracting the interest of the physicists since it was proposed. Schrodinger's Cat paradox is a thought experiment that entangles a cat with some decay atoms, in which the entanglement between the macroscopic object and the microscopic atoms is established. Mac-micro entanglement relates to some important problems in quantum physics. It is more likely to interact with the surroundings for the quantum system as its size increases, which is the reason why we hardly observe the macroscopic superposition state. Can the superposition state theory of quantum physics be used in macro domain? Is there a limitation to the scale for the objects in the superposition states? These questions need studying and verifying in experiment. In addition, the preparation of the macro-micro entanglement state provides a new possibility to study the decoherence model. Macro-micro entanglement can be realized in many physical systems, such as atomic ensembles, superconducting circuits, electro-mechanical and opto-mechanical systems. Here in this paper we will introduce the development of macro-micro entanglement in optical system. The initial approach to creating the macro-micro entanglement in the context of optical system is quantum cloning by simulating the emission. Then the quantum-injected optical parametric amplification is used to amplify single photon to a macroscopic level. Afterwards, the displacement in phase space is proposed to create the macro-micro entanglement. Since the photon number of the macro-micro entanglement with the optical parametric amplification approach can be about 104, the studies towards the detection of this type of entanglement with human eyes have been extensively conducted. But it is realized that the coarse-grained measurements, such as those with the human eye, generally cannot judge whether macro-micro entanglement exists, and hence cannot be used to prove the considered type of micro-macro entanglement. A way of overcoming this difficulty is to invert the amplification process, bringing the macro system back to the micro level. The entanglement can then be verified by using single-photon detectors. Because local operation and classical communication cannot create entanglement, the de-amplification process will not increase the entanglement and the presence of the entanglement in the end shows that entanglement is present between the amplification and de-amplification process. Inspired by this thought, two groups create and verify mac-micro entanglement between one photon and 108 photons. What they used to amplify the micro states is the displacement operation in phase space, which can be realized by combining a single photon state and a coherent state with a highly asymmetric beam splitter. Because the entanglement is a precondition for a secure quantum key distribution, and the macro-micro entanglement has more photons than the traditional micro entanglement, we will discuss the possibility whether the macro-micro entanglement can be used in quantum key distribution and improve the distance of the quantum key distribution. We point out that the mac-micro entanglement and the binary reverse reconciliation continuous variable quantum key distribution protocol are the same in physics essence. We will introduce a quantum key distribution scheme with two phase entangled coherent states. Although the security proof of the scheme is not complete, it still provides us with the possibility to use the macro-micro entanglement in quantum key distribution.
[1] Bassi A, Lochan K, Satin S, Singh T P, Ulbricht H 2013 Rev. Mod. Phys. 85 471
[2] Julsgaard B, Kozhekin A, Polzik E S 2001 Nature 413 400
[3] Neeley M, Ansmann M, Bialczak R C, Hofheinz M, Katz N, Lucero E, O’Connell A, Wang H, Cleland A, Martinis J M 2008 Nat. Phys. 4 523
[4] O’Connell A D, Hofheinz M, Ansmann M, Bialczak R C, Lenander M, Lucero E, Neeley M, Sank D, Wang H, Weides M 2010 Nature 464 697
[5] Verhagen E, Delelise S, Weis S, Schliesser A, Kippenberg T J 2012 Nature 482 63
[6] Simon C, Weihs G, Zeilinger A 2000 Phys. Rev. Lett. 84 2993
[7] de Martini F, Mussi V, Bovino F 2000 Opt. Comm. 179 581
[8] Lamas-Linares A, Simon C, Howell J C, Bouwmeester D 2002 Science 296 712
[9] de Martini F 1998 Phys. Rev. Lett. 81 2842
[10] de Martini F, Sciarrino F, Vitelli C 2008 Phys. Rev. Lett. 100 253601
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[12] Brunner N, Cavalcanti D, Pironio S, Scarani V, Wehner S 2014 Rev. Mod. Phys. 86 419
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[15] Sekatski P, Sanguinetti B, Pomarico E, Gisin N, Simon C 2010 Phys. Rev. A 82 053814
[16] Simon C 2013 Quantum Information and Measurement (New York：Rochester) June 17-20, 2013 Th2B.1
[17] Raeisi S, Tittel W, Simon C 2012 Phys. Rev. Lett. 108 120404
[18] Ghobadi R, Lvovsky A, Simon C 2013 Phys. Rev. Lett. 110 170406
[19] Wootters W K 1998 Phys. Rev. Lett. 80 2245
[20] Sekatski P, Sangouard N, Stobinska M, Bussieres F, Afzelius M, Gisin N 2012 Phys. Rev. A 86 060301
[21] Bruno N, Martin A, Sekatski P, Sangouard N, Thew R, Gisin N 2013 Nat. Phys. 9 545
[22] Lvovsky A, Ghobadi R, Chandra A, Prasad A, Simon C 2013 Nat. Phys. 9 541
[23] Chou C W, de Riedmatten H, Felinto D, Polyakov S V, van Enk S J, Kimble H J 2005 Nature 438 828
[24] Ghobadi R, Kumar S, Pepper B, Bouwmeester D, Lvovsky A, Simon C 2014 Phys. Rev. Lett. 112 080503
[25] Curty M, Lewenstein M, Lukenhaus N 2004 Phys. Rev. Lett. 92 217903
[26] Kirby B, Franson J 2014 Phys. Rev. A 89 033861
[27] Grosshans F, Acin A, Cerf N 2007 Quantum Information with Continuous Variables of Atoms and Light (London：Imperial College Press) pp63-83
[28] Zhang Y S, Guo G C 2006 Chin. Phys. Lett. 23 1372
[29] Chen J J, Han Z F, Zhao Y B, Gui Y Z, Guo G C 2006 Physics 35 785 (in Chinese) [陈进建, 韩正甫, 赵义博, 桂有珍, 郭光灿 2006 物理 35 785]
[30] Zhao Y B 2009 Ph. D. Dissertation (Hefei: Univesity of Science and Technology Of China) (in Chinese) [赵义博 2009 博士学位论文 (合肥：中国科学技术大学)]
[31] Simon D S, Jaeger G, Sergienko A V 2014 Phys. Rev. A 89 012315
[32] Nemoto K, Munro W J 2004 Phys. Rev. Lett. 93 250502
[33] Munro W J, Nemoto K, Spiller T P 2005 New J. Phys. 7 137
[34] Fiurášek J 2001 Phys. Rev. Lett. 86 4942
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[1] Bassi A, Lochan K, Satin S, Singh T P, Ulbricht H 2013 Rev. Mod. Phys. 85 471
[2] Julsgaard B, Kozhekin A, Polzik E S 2001 Nature 413 400
[3] Neeley M, Ansmann M, Bialczak R C, Hofheinz M, Katz N, Lucero E, O’Connell A, Wang H, Cleland A, Martinis J M 2008 Nat. Phys. 4 523
[4] O’Connell A D, Hofheinz M, Ansmann M, Bialczak R C, Lenander M, Lucero E, Neeley M, Sank D, Wang H, Weides M 2010 Nature 464 697
[5] Verhagen E, Delelise S, Weis S, Schliesser A, Kippenberg T J 2012 Nature 482 63
[6] Simon C, Weihs G, Zeilinger A 2000 Phys. Rev. Lett. 84 2993
[7] de Martini F, Mussi V, Bovino F 2000 Opt. Comm. 179 581
[8] Lamas-Linares A, Simon C, Howell J C, Bouwmeester D 2002 Science 296 712
[9] de Martini F 1998 Phys. Rev. Lett. 81 2842
[10] de Martini F, Sciarrino F, Vitelli C 2008 Phys. Rev. Lett. 100 253601
[11] Raeisi S, Sekatski P, Simon C 2011 Phys. Rev. Lett. 107 250401
[12] Brunner N, Cavalcanti D, Pironio S, Scarani V, Wehner S 2014 Rev. Mod. Phys. 86 419
[13] Rieke F, Baylor D 1998 Rev. Mod. Phys. 70 1027
[14] Sekatski P, Brunner N, Branciard C, Gisin N, Simon C 2009 Phys. Rev. Lett. 103 113601
[15] Sekatski P, Sanguinetti B, Pomarico E, Gisin N, Simon C 2010 Phys. Rev. A 82 053814
[16] Simon C 2013 Quantum Information and Measurement (New York：Rochester) June 17-20, 2013 Th2B.1
[17] Raeisi S, Tittel W, Simon C 2012 Phys. Rev. Lett. 108 120404
[18] Ghobadi R, Lvovsky A, Simon C 2013 Phys. Rev. Lett. 110 170406
[19] Wootters W K 1998 Phys. Rev. Lett. 80 2245
[20] Sekatski P, Sangouard N, Stobinska M, Bussieres F, Afzelius M, Gisin N 2012 Phys. Rev. A 86 060301
[21] Bruno N, Martin A, Sekatski P, Sangouard N, Thew R, Gisin N 2013 Nat. Phys. 9 545
[22] Lvovsky A, Ghobadi R, Chandra A, Prasad A, Simon C 2013 Nat. Phys. 9 541
[23] Chou C W, de Riedmatten H, Felinto D, Polyakov S V, van Enk S J, Kimble H J 2005 Nature 438 828
[24] Ghobadi R, Kumar S, Pepper B, Bouwmeester D, Lvovsky A, Simon C 2014 Phys. Rev. Lett. 112 080503
[25] Curty M, Lewenstein M, Lukenhaus N 2004 Phys. Rev. Lett. 92 217903
[26] Kirby B, Franson J 2014 Phys. Rev. A 89 033861
[27] Grosshans F, Acin A, Cerf N 2007 Quantum Information with Continuous Variables of Atoms and Light (London：Imperial College Press) pp63-83
[28] Zhang Y S, Guo G C 2006 Chin. Phys. Lett. 23 1372
[29] Chen J J, Han Z F, Zhao Y B, Gui Y Z, Guo G C 2006 Physics 35 785 (in Chinese) [陈进建, 韩正甫, 赵义博, 桂有珍, 郭光灿 2006 物理 35 785]
[30] Zhao Y B 2009 Ph. D. Dissertation (Hefei: Univesity of Science and Technology Of China) (in Chinese) [赵义博 2009 博士学位论文 (合肥：中国科学技术大学)]
[31] Simon D S, Jaeger G, Sergienko A V 2014 Phys. Rev. A 89 012315
[32] Nemoto K, Munro W J 2004 Phys. Rev. Lett. 93 250502
[33] Munro W J, Nemoto K, Spiller T P 2005 New J. Phys. 7 137
[34] Fiurášek J 2001 Phys. Rev. Lett. 86 4942
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