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量子相干不仅是量子力学中的一个基本概念, 同时也是重要的量子信息处理的物理资源. 随着基于资源理论框架的量子相干度量方案的提出, 量子相干度的量化研究成为近年来人们关注的一个热点问题. 量子相干作为一种物理资源也十分脆弱, 极容易受到环境噪声的影响而产生退相干, 因此开放系统中的量子相干演化和保持也是人们广泛关注的课题. 另外, 量子相干在量子多体系统、量子热动力学、量子生物学等领域也有着潜在的应用价值. 本文介绍量子相干度量的资源理论框架和基于该框架定义的相对熵相干性、l1范数相干性、基于量子纠缠的相干性、基于凸顶结构的相干性和相干鲁棒性等量子相干度量函数, 概述开放系统中量子相干演化的动力学行为、典型信道的量子相干产生和破坏能力以及量子相干的冻结等现象, 同时例举量子相干在Deutsch-Jozsa算法、Grover算法以及量子多体系统相变问题研究等方面的重要应用. 量子相干研究仍处于快速发展之中, 期望本综述能为该领域的发展带来启示.Quantum coherence is not only a fundamental concept of quantum mechanics, but also an important physical resource for quantum information processing. Along with the formulation of the resource theoretic framework of quantum coherence, the quantification of coherence is still one of the recent research focuses. Quantum coherence is also very fragile, and the environmental noise usually induces a system to decohere. Hence it is also an important subject to make clear the dynamical behavior and to seek a flexible way of preserving quantum coherence of an open quantum system. Besides, there are many potential applications of quantum coherence in quantum many-body system, quantum thermodynamics, quantum biology and other related fields. We review in this paper the resource theoretic framework for quantifying coherence and the relevant quantum coherence measures defined within this framework which includes the relative entropy of coherence, the l1 norm of coherence, the entanglement-based measure of coherence, the convex roof measure of coherence, and the robustness of coherence. We also review the dynamical behaviors of quantum coherence for certain open quantum systems, the coherence generating and breaking power of typical quantum channels, and the freezing phenomenon of quantum coherence. Moreover, we exemplify applications of quantum coherence in Deutsch-Jozsa algorithm, Grover search algorithms, and the study of quantum phase transitions in multipartite systems. We hope that these results may provide not only an overview of the relevant field, but also an outlook of the future research direction of this exciting field.
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Keywords:
- quantum coherence /
- resource theory /
- quantum information
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[1] Hu M L, Hu X, Wang J, Peng Y, Zhang Y R, Fan H 2018 Phys. Rep. 762 1Google Scholar
[2] Aberg J 2014 Phys. Rev. Lett. 113 150402Google Scholar
[3] Lostaglio M, Jennings D, Rudolph T 2015 Nat. Commun. 6 6383Google Scholar
[4] Narasimhachar V, Gour G 2015 Nat. Commun. 6 7689Google Scholar
[5] Lambert N, Chen Y N, Cheng Y C, Li C M, Chen G Y, Nori F 2013 Nat. Phys. 9 10Google Scholar
[6] Baumgratz T, Cramer M, Plenio M B 2014 Phys. Rev. Lett. 113 140401Google Scholar
[7] Streltsov A, Singh U, Dhar H S, Bera M N, Adesso G 2015 Phys. Rev. Lett. 115 020403Google Scholar
[8] Napoli C, Bromley T R, Cianciaruso M, Piani M, Johnston N, Adesso G 2016 Phys. Rev. Lett. 116 150502Google Scholar
[9] Bu K, Anand N, Singh U 2018 Phys. Rev. A 97 032342Google Scholar
[10] Yu C S 2017 Phys. Rev. A 95 042337Google Scholar
[11] Yuan X, Zhou H, Cao Z, Ma X 2015 Phys. Rev. A 92 022124Google Scholar
[12] Qi X, Gao T, Yan F L 2017 J. Phys. A 50 285301Google Scholar
[13] Liu C L, Zhang D J, Yu X D, Ding Q M 2017 Quantum Inf. Process. 16 198Google Scholar
[14] Bromley T R, Cianciaruso M, Adesso G 2015 Phys. Rev. Lett. 114 210401Google Scholar
[15] Hu M L, Fan H 2016 Sci. Rep. 6 29260Google Scholar
[16] Zanardi P, Styliaris G, Venuti L C 2017 Phys. Rev. A 95 052306Google Scholar
[17] Horodecki R, Horodecki P, Horodecki M, Horodecki K 2009 Rev. Mod. Phys. 81 865Google Scholar
[18] Winter A, Yang D 2016 Phys. Rev. Lett. 116 120404Google Scholar
[19] Shao L H, Xi Z, Fan H, Li Y 2015 Phys. Rev. A 91 042120Google Scholar
[20] Yao Y, Xiao X, Ge L, Li M, Sun C P 2015 Phys. Rev. A 92 022112Google Scholar
[21] Streltsov A, Rana S, Boes P, Eisert J 2017 Phys. Rev. Lett. 119 140402Google Scholar
[22] Aberg J 2006 arXiv:0612146 [quant-ph]
[23] Chitambar E, Gour G 2016 Phys. Rev. Lett. 117 030401Google Scholar
[24] Chitambar E, Gour G 2016 Phys. Rev. A 94 052336Google Scholar
[25] Marvian I, Spekkens R W 2016 Phys. Rev. A 94 052324Google Scholar
[26] de Vincenzo J I, Streltsov A 2017 J. Phys. A 50 045301Google Scholar
[27] Yu X D, Zhang D J, Xu G F, Tong D M 2016 Phys. Rev. A 94 060302Google Scholar
[28] Du S, Bai Z, Guo Y 2015 Phys. Rev. A 91 052120Google Scholar
[29] Peng Y, Jiang Y, Fan H 2016 Phys. Rev. A 93 032326Google Scholar
[30] Rastegin A E 2016 Phys. Rev. A 93 032136Google Scholar
[31] Hu M L, Fan H 2017 Phys. Rev. A 95 052106Google Scholar
[32] Yao Y, Dong G H, Ge L, Li M, Sun C P 2016 Phys. Rev. A 94 062339Google Scholar
[33] Singh U, Bera M N, Dhar H S, Pati A K 2015 Phys. Rev. A 91 052115Google Scholar
[34] Rana S, Parashar P, Lewenstein M 2016 Phys. Rev. A 93 012110Google Scholar
[35] Streltsov A, Kampermann H, Bruß D 2010 New J. Phys. 12 123004Google Scholar
[36] Marvian I, Spekkens R W 2014 Nat. Commun. 5 3821Google Scholar
[37] Marvian I, Spekkens R W, Zanardi P 2016 Phys. Rev. A 93 052331Google Scholar
[38] Zhang Y R, Shao LH, Li Y, Fan H 2016 Phys. Rev. A 93 012334Google Scholar
[39] Xu J 2016 Phys. Rev. A 93 032111Google Scholar
[40] Tan K C, Volkoff T, Kwon H, Jeong H 2017 Phys. Rev. Lett. 119 190405Google Scholar
[41] Silva I A, Souza A M, Bromley T R, Cianciaruso M, Marx R, Sarthour R S, Oliveira I S, Franco R L, Glaser S J, deAzevedo E R, Soares-Pinto D O, Adesso G 2016 Phys. Rev. Lett. 117 160402Google Scholar
[42] Mani A, Karimipour V 2015 Phys. Rev. A 92 032331Google Scholar
[43] Bu K, Kumar A, Zhang L, Wu J 2017 Phys. Lett. A 381 1670Google Scholar
[44] Xi Z J, Hu M L, Li Y M, Fan H 2018 Quantum Inf. Process. 17 34Google Scholar
[45] Situ H, Hu X 2016 Quantum Inf. Process. 15 4649Google Scholar
[46] Andersson E, Cresser J D, Hall M J W 2007 J. Mod. Opt. 54 1695Google Scholar
[47] Deutsch D, Jozsa R 1992 Proc. R. Soc. Landon A 439 553Google Scholar
[48] Hillery M 2016 Phys. Rev. A 93 012111Google Scholar
[49] Anand N, Pati A K 2016 arXiv:1611.04542 [quant-ph]
[50] Shi H L, Liu S Y, Wang X H, Yang W L, Yang Z Y, Fan H 2017 Phys. Rev. A 95 032307Google Scholar
[51] Karpat G, Çakmak B, Fanchini F F 2014 Phys. Rev. B 90 104431Google Scholar
[52] Chen J J, Cui J, Zhang Y R, Fan H 2016 Phys. Rev. A 94 022112Google Scholar
[53] Lei S, Tong P 2016 Quantum Inf. Process. 15 1811Google Scholar
[54] Li Y C, Lin H Q 2016 Sci. Rep. 6 26365Google Scholar
[55] Malvezzi A L, Karpat G, Çakmak B, Fanchini F F, Debarba T, Vianna R O 2016 Phys. Rev. B 93 184428Google Scholar
[56] Faist P, Oppenheim J, Renner R 2015 New J. Phys. 17 043003Google Scholar
[57] Misra A, Singh U, Bhattacharya S, Pati A K 2016 Phys. Rev. A 93 052335Google Scholar
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