利用量子相干性判定开放二能级系统中非马尔可夫性

贺志; 李莉; 姚春梅; 李艳

doi:10.7498/aps.64.140302

摘要

从量子相干性包括l1 norm相干性和量子相对熵相干性的角度建立了判定开放量子系统中非马尔可夫过程的方法, 并给出了相应的判别条件. 作为它们的具体应用, 研究了一个两能级系统分别经历相位衰减通道、随机幺正通道和振幅耗散通道作用时对应的非马尔可夫过程发生必须满足的条件. 对于三种通道模型, 得到了l1 norm相干性对系统任意态非马尔可夫过程发生的判别条件, 并发现在相位衰减通道和振幅耗散通道中其非马尔可夫过程发生的条件与用其他方式如信息回流、可分性和量子互熵给出的条件是相同的, 而在随机幺正通道中给出了一个新的且不完全等价于基于信息回流和可分性对应的条件. 至于量子相对熵相干性, 在相位衰减通道中得到了对系统任意态的非马尔可夫过程发生的具体条件, 并发现该条件也等同于基于信息回流、可分性和量子互熵给出的条件. 而在随机幺正通道和振幅耗散通道中得到了系统最大相干态对应的非马尔可夫过程发生的条件.

关键词:

Abstract

We propose an approach to measuring non-Markovianity of an open two-level system from quantum coherence perspective including l1 norm of coherence and quantum relative entropy of coherence, and derive corresponding non-Markovian conditions. Further, as a particular application, non-Markovian conditions of an open two-level system undergoing phase damping channel, random unitary channel and amplitude damping channel, respectively are investigated. Specifically speaking, for the three channels we obtain non-Markovian conditions based on l1 norm of coherence at any initial state of system, and find that non-Markovian conditions are the same as the conditions of other measurements, i.e., information back-flow, divisibility and quantum mutual entropy for the phase damping channel and amplitude damping channel, but non-Markovian conditions new and different from the conditions of other measurements for random unitary channel. On the other hand, for phase damping channel we obtain non-Markovian conditions based on quantum relative entropy of coherence at any initial state of system, which are the same as the conditions of other measures, i.e., information back-flow, divisibility and quantum mutual entropy. However, for the random unitary channel and amplitude damping channel we obtain non-Markovian conditions at maximally coherent state of system.

Keywords:

作者及机构信息

1.
湖南文理学院物理与电子科学学院, 常德 415000

基金项目: 国家自然科学基金(批准号：61475045, 11404111)、湖南省自然科学基金青年项目(批准号：2015JJ3092)、湖南省教育厅一般项目(批准号：12C0826)和湖南文理学院重点项目(批准号：14ZD01)资助的课题．

Authors and contacts

1.
College of Physics and Electronics, Hunan University of Arts and Science, Changde 415000, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61475045, 11404111), the Natural Science Foundation of Hunan Province, China (Grant No. 2015JJ3092), the Research Foundation of Education Bureau of Hunan Province, China (Grant No. 12C0826), and the School Foundation from the Hunan University of Arts and Science, China (Grant No. 14ZD01).

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施引文献

[1]	Buluta I, Ashhab S, Nori F 2011 Rep. Prog. Phys. 74 104401
[2]	Bellomo B, LoFranco R, Compagno G 2007 Phys. Rev. Lett. 99 160502
[3]	Zhang Y J, Man Z X, Xia Y J 2009 Eur. Phys. J. D 55 173
[4]	Xiao X, Fang M F, Li Y L, Zeng K, Wu C 2009 J. Phys. B: At. Mol. Opt. Phys. 42 235502
[5]	Xiao X, Fang M F, Li Y L 2010 J. Phys. B: At. Mol. Opt. Phys. 43 185505
[6]	Han W, Cui W K, Zhang Y J, Xia Y J 2012 Acta Phys. Sin. 61 230302 (in Chinese) [韩伟, 崔文凯, 张英杰, 夏云杰 2012 61 230302]
[7]	Shan C J, Liu J B, Chen T, Liu T K, Huang Y X, Li H 2010 Chin. Phys. Lett. 27 100301
[8]	Xiao X, Fang M F, Li Y L, Kang G D, Wu C 2010 Opt. Commun. 283 3001
[9]	Li C F, Wang H T, Yuan H Y, Ge R C, Guo G C 2011 Chin. Phys. Lett. 28 120302
[10]	Han W, Zhang Y J, Xia Y J 2013 Chin. Phys. B 22 010306
[11]	He Z, Li L W 2013 Acta Phys. Sin. 62 180301 (in Chinese) [贺志, 李龙武 2013 62 180301]
[12]	Zheng L M, Wang F Q, Liu S H 2009 Acta Phys. Sin. 58 2430 (in Chinese) [郑力明, 王发强, 刘颂豪 2009 58 2430]
[13]	Xiao X, Fang M F, Hu Y M 2011 Phys. Scr. 84 045011
[14]	Cai C J, Fang M F, Xiao X, Huang J 2012 Acta Phys. Sin. 61 210303 (in Chinese) [蔡诚俊, 方卯发, 肖兴, 黄江 2012 61 210303]
[15]	Breuer H P, Laine E M, Piilo J 2009 Phys. Rev. Lett. 103 210401
[16]	Rivas A, Huelga S F, Plenio M B 2010 Phys. Rev. Lett. 105 050403
[17]	Lu X M, Wang X G, Sun C P 2010 Phys. Rev. A 82 042103
[18]	Hou S C, Yi X X, Yu S X, Oh C H 2011 Phys. Rev. A 83 062115
[19]	Luo S, Fu S, Song H 2012 Phys. Rev. A 86 044101
[20]	Lorenzo S, Plastina F, Paternostro M 2013 Phys. Rev. A 88 020102
[21]	Bylicka B, Chruscinski D, Maniscalco S 2014 Sci. Rep. 4 5720
[22]	Chruscinski D, Maniscalco 2014 Phys. Rev. A 112 120404
[23]	Liu J, Lu X M, Wang X G 2013 Phys. Rev. A 87 042103
[24]	He Z, Yao C, Zou J 2014 Phys. Rev. A 90 042101
[25]	Liu B H, Li L, Huang Y F, Li C F, Guo G C, Laine E M, Breuer H P, Piilo J 2011 Nat. Phys. 7 931
[26]	Tang J S, Li C F, Li Y L, Zou X B, Guo G C 2012 Europhys. Lett. 97 10002
[27]	Xu Z Y, Yang W L, Feng M 2010 Phys. Rev. A 81 044105
[28]	He Z, Zou J, Li L, Shao B 2011 Phys. Rev. A 83 012108
[29]	Zeng H S, Tang N, Zheng Y P, Wang G Y 2011 Phys. Rev. A 84 032118
[30]	Haikka P, Cresser J D, Maniscalco S 2011 Phys. Rev. A 83 012112.
[31]	Chruscinski D, Wudarski F 2013 Phys. Lett. A 377 1425
[32]	Jiang M, Luo S 2013 Phys. Rev. A 88 034101
[33]	Baumgratz T, Cramer M, Plenio M B 2014 Phys. Rev. Lett. 113 140401
[34]	Girolami D 2014 Phys. Rev. Lett. 113 170401
[35]	Lindblad G 1975 Commun. Math. Phys. 40 147
[36]	Ruskai M B 2002 J. Math. Phys. 43 4358
[37]	Vedral V, Plenio M B 1997 Phys. Rev. A 57 1619
[38]	Wolf M M, Eisert J, Cubitt T S, Cirac J I 2008 Phys. Rev. Lett. 101 150402
[39]	Shao L H, Xi Z J, Fan H, Li Y M 2015 Phys. Rev. A 91 042120
[40]	Breuer H P, Petruccione F 2002 The Theory of Open Quantum Systems (Oxford: Oxford University Press) p472
[41]	Vacchini B 2012 J. Phys. B: At. Mol. Opt. Phys. 45 154007
[42]	Giovannetti V, Lloyd S, Maccone L 2006 Phys. Rev. Lett. 96 010401
[43]	Xi Z J, Li Y M, Fan H 2014 arXiv 1408.3194v2 [quant-ph]
[44]	Du S, Bei Z, Guo Y 2015 Phys. Rev. A 91 052120
[45]	Bromley T R, Cianciaruso M, Adesso G 2015 Phys. Rev. Lett. 114 210401
[46]	Zhang Y J, Han W, Xia Y J, Yu Y M, Fan H 2015 arXiv 1502.02446v1 [quant-ph]

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