Non-Markovianity of open two-level system by means of quantum coherence

He Zhi; Li Li; Yao Chun-Mei; Li Yan

doi:10.7498/aps.64.140302

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:

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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Cited By

[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 物理学报 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 物理学报 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 物理学报 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 物理学报 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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Vol. 64, Issue 14 - 2015-07-20

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