一种基于非局域性的量子通信的研究
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摘要
量子通信是指利用量子效应加密并进行信息传输的一种通信方式,已逐步从理论走向实验,并向实用化发展,高效安全的信息传输日益受到人们的关注。1993年,6位来自不同国家的科学家,提出了利用经典与量子相结合的方法实现量子隐形传态的方案。在这个方案中,纠缠态的非局域性起着至关重要的作用,这种超出人们普通认知范畴的特性,构成了保密量子通信的基础,复合系统正交量子态不一定能被局域区分是量子非局域性的重要表现形式之一。文章致力于研究d■d中相互正交乘积基量子态的局域不可区分性。文章针对a■d (d>2)量子系统,构造了另一类局域不可区分的正交乘积基量子态,其包含3(d-1)个正交乘积态,并可用一种简单有效的方法证明这些状态是局域不可区分的,这个结果也可用于说明无纠缠的非局域现象.
Quantum communication is a kind of communication method which encrypts and transmits information by using quantum effect. The subject has gradually moved from theory to experiment, and has developed to practicality. People pay more and more attention to efficient and secure information transmission. In 1993, six scientists from different countries proposed a scheme to realize quantum teleportation by combining classical and quantum methods. In this scheme, the nonlocality of entangled states plays an important role. This characteristic beyond ordinary cognition constitutes the basic resource of secure quantum communication. Orthogonal quantum states of composite systems may not be locally distinguished as one of the important manifestations of quantumnonlocality.This paper is devoted to thestudy of the local indistinguishability of orthogonal product basis quantum states ind ■d. In this paper, we construct another class of local indistinguishable orthogonal product basis quantum state fora ■d(d>2) quantum systems, which contain 3(d-1)orthogonal product states. We will prove that these states are locally indistinguishable by a simple and efficient method.This result also demonstrates the phenomenon of nonlocality without entanglement.
Quantum communication is a kind of communication method which encrypts and transmits information by using quantum effect. The subject has gradually moved from theory to experiment, and has developed to practicality. People pay more and more attention to efficient and secure information transmission. In 1993, six scientists from different countries proposed a scheme to realize quantum teleportation by combining classical and quantum methods. In this scheme, the nonlocality of entangled states plays an important role. This characteristic beyond ordinary cognition constitutes the basic resource of secure quantum communication. Orthogonal quantum states of composite systems may not be locally distinguished as one of the important manifestations of quantumnonlocality.This paper is devoted to thestudy of the local indistinguishability of orthogonal product basis quantum states ind ■d. In this paper, we construct another class of local indistinguishable orthogonal product basis quantum state fora ■d(d>2) quantum systems, which contain 3(d-1)orthogonal product states. We will prove that these states are locally indistinguishable by a simple and efficient method.This result also demonstrates the phenomenon of nonlocality without entanglement.
引文
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[12]YANG Y H, Gao F, TIAN G J, et al.Local Distinguishability of Orthogonal Quantum States in a 2(?)2(?)2 System[J].Physical Review A, 2013, 88(2):1-4.
[13] LEBL J,SHAKEEL A,WALLACH N.Local Distinguishability of Generic Unentangled Orthonormal Bases[J]. Physical Review A,2016, 93(1):1-6.
[14] WALGATE J, HARDY L.Nonlocality, Asymmetry, and Distinguishing Bipartite States[J].Physical Review Letters, 2002,89(14):1-4.
[15] CHEN P X,LI C Z.Distinguishing the Elements of a Full Product Basis Set Needs Only Projective Measurements and Classical Communication[J].Physical Review A, 2004, 70(2):1-4.
[16] WATROUS J.Bipartite Subspaces Having no Bases Distinguishable by Local Operations and Classical Communication[J].Physical Review Letters, 2005, 95(8):1-4.
[17] FENG Y, SHI Y.Characterizing Locally Indistinguishable Orthogonal Product States.[J].IEEE Trans, 2007, 55(6):2799-2806.
[18] WALGATE J,HARDY L.Nonlocality, Asymmetry, and Distinguishing Bipartite States[J].Physical Review Letters, 2002,89(14):1-4.
[19] ZHANG Z C,GAO F, TIAN GJ,et al.Nonlocality of Orthogonal Product Basis Quantum States[J].Physical Review A,2014, 90(2):1-4.
[20] ZHANG Z C, GAO F, QIN S J, et al.Nonlocality of Orthogonal Product States[J].Physical Review A, 2015, 92(1):1-4.
[21] YU S, OH C H.Detecting the Local Indistinguishability of Maximally Entangled States[EB/OL].https://www.researchgate.net/publication/27185525 8_Detecting_the_local_indistinguishability_of_maximally_entangled_states, 2018-5-15.
[22] ZHANG Z C, SONG Y Q, SONG T T, et al.Local Distinguishability of Orthogonal Quantum States with Multiple Copies of2(?)2Maximally Entangled States[J].Physical Review A,2018, 97(2):1-7.
[2] FENG K.Unextendible Product Bases and 1-factorization ofComplete Graphs[J]. Disc. Appl. Math,2006, 15(4):942-949.
[3] DUANR Y, FENG Y, XIN Y, et al.Distinguishability of Quantum States by Separable Operations[J].IEEETrans,2009,55(3):1320-1330.
[4] LV Xingfeng, JIANG Yu.Development of the Encryption Technology of Computer Cryptography[J].Netinfo Security, 2009,9(4):29-32.吕兴凤,姜誉.计算机密码学中的加密技术研究进展[J].信息网络安全,2009,9(4):29-32.
[5] GAO F, LIU B, HUANG W, et al.Postprocessing of the Oblivious Key in Quantum Private Query[J].IEEE Journal of Selected Topics in Quantum Electronics, 2014, 21(3):98-108.
[6] WEI C Y, WANG T Y, GAO F.Practical Quantum Private Query with Better Performance in Resisting Joint-measurement Attack[J].Physical Review A, 2016, 93(4):1-7.
[7] LIU Chengji, LI Zhihui, SI Mengmeng, et al.Quantum-secretsharing Scheme Based on Local Distinguishability of Orthogonal Six-qudit Entangled States[J].Netinfo Security, 2018, 18(4):56-64.刘成基,李志慧,司萌萌,等.基于局域区分的六粒子正交纠缠态的量子秘密共享方案[J].信息网络安全,2018, 18(4):56-64.
[8] WALGATE J, SHORT A J, HARDY L, et al.Local Distinguishability of Multipartite Orthogonal Quantum States[J].Physical Review Letters, 2000, 85(23):4972-4975.
[9] YE M Y, JIANG W, CHEN P X, et al. Local Distinguishability of Orthogonal Quantum States and Generators of SU(N)[J].Physical Review A, 2007, 76(3):1-5.
[10] BANDYOPADHYAY S, WALGATE J. Local Distinguishability of Any Three Quantum States[J]. Journal of Physics A Mathematical&Theoretical,2009, 42(7):1-4.
[11] BANDYOPADHYAY S,Entanglement, Mixedness, and Perfect Local Discrimination of Orthogonal Quantum States[J].Physical Review A, 2012,85(2):1-6.
[12]YANG Y H, Gao F, TIAN G J, et al.Local Distinguishability of Orthogonal Quantum States in a 2(?)2(?)2 System[J].Physical Review A, 2013, 88(2):1-4.
[13] LEBL J,SHAKEEL A,WALLACH N.Local Distinguishability of Generic Unentangled Orthonormal Bases[J]. Physical Review A,2016, 93(1):1-6.
[14] WALGATE J, HARDY L.Nonlocality, Asymmetry, and Distinguishing Bipartite States[J].Physical Review Letters, 2002,89(14):1-4.
[15] CHEN P X,LI C Z.Distinguishing the Elements of a Full Product Basis Set Needs Only Projective Measurements and Classical Communication[J].Physical Review A, 2004, 70(2):1-4.
[16] WATROUS J.Bipartite Subspaces Having no Bases Distinguishable by Local Operations and Classical Communication[J].Physical Review Letters, 2005, 95(8):1-4.
[17] FENG Y, SHI Y.Characterizing Locally Indistinguishable Orthogonal Product States.[J].IEEE Trans, 2007, 55(6):2799-2806.
[18] WALGATE J,HARDY L.Nonlocality, Asymmetry, and Distinguishing Bipartite States[J].Physical Review Letters, 2002,89(14):1-4.
[19] ZHANG Z C,GAO F, TIAN GJ,et al.Nonlocality of Orthogonal Product Basis Quantum States[J].Physical Review A,2014, 90(2):1-4.
[20] ZHANG Z C, GAO F, QIN S J, et al.Nonlocality of Orthogonal Product States[J].Physical Review A, 2015, 92(1):1-4.
[21] YU S, OH C H.Detecting the Local Indistinguishability of Maximally Entangled States[EB/OL].https://www.researchgate.net/publication/27185525 8_Detecting_the_local_indistinguishability_of_maximally_entangled_states, 2018-5-15.
[22] ZHANG Z C, SONG Y Q, SONG T T, et al.Local Distinguishability of Orthogonal Quantum States with Multiple Copies of2(?)2Maximally Entangled States[J].Physical Review A,2018, 97(2):1-7.