Quantum speed limits of a qubit system interacting with a nonequilibrium environment

doi:10.1088/1674-1056/25/8/080304

中国物理B ›› 2016, Vol. 25 ›› Issue (8): 80304-080304.doi: 10.1088/1674-1056/25/8/080304

Quantum speed limits of a qubit system interacting with a nonequilibrium environment

Zhi He(贺志), Chun-Mei Yao(姚春梅), Li Li(李莉), Qiong Wang(王琼)

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

收稿日期:2016-02-28 修回日期:2016-05-03 出版日期:2016-08-05 发布日期:2016-08-05
通讯作者: Zhi He E-mail:hz9209@126.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grants Nos. 61505053 and 61475045), the Natural Science Foundation of Hunan Province, China(Grant No. 2015JJ3092), the School Foundation from the Hunan University of Arts and Science (Grant No. 14ZD01), the Fund from the Key Laboratory of Photoelectric Information Integration and Optical Manufacturing Technology of Hunan Province, China, and the Construction Program of the Key Discipline in Hunan University of Arts and Science (Optics).

Quantum speed limits of a qubit system interacting with a nonequilibrium environment

Zhi He(贺志), Chun-Mei Yao(姚春梅), Li Li(李莉), Qiong Wang(王琼)

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

Received:2016-02-28 Revised:2016-05-03 Online:2016-08-05 Published:2016-08-05
Contact: Zhi He E-mail:hz9209@126.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grants Nos. 61505053 and 61475045), the Natural Science Foundation of Hunan Province, China(Grant No. 2015JJ3092), the School Foundation from the Hunan University of Arts and Science (Grant No. 14ZD01), the Fund from the Key Laboratory of Photoelectric Information Integration and Optical Manufacturing Technology of Hunan Province, China, and the Construction Program of the Key Discipline in Hunan University of Arts and Science (Optics).

摘要/Abstract

摘要： The speed of evolution of a qubit undergoing a nonequilibrium environment with spectral density of general ohmic form is investigated. First we reveal non-Markovianity of the model, and find that the non-Markovianity quantified by information backflow of Breuer et al. [Phys. Rev. Lett. 103 210401 (2009)] displays a nonmonotonic behavior for different values of the ohmicity parameter s in fixed other parameters and the maximal non-Markovianity can be achieved at a specified value s. We also find that the non-Markovianity displays a nonmonotonic behavior with the change of a phase control parameter. Then we further discuss the relationship between quantum speed limit (QSL) time and non-Markovianity of the open-qubit system for any initial states including pure and mixed states. By investigation, we find that the QSL time of a qubit with any initial states can be expressed by a simple factorization law: the QSL time of a qubit with any qubit-initial states are equal to the product of the coherence of the initial state and the QSL time of maximally coherent states, where the QSL time of the maximally coherent states are jointly determined by the non-Markovianity, decoherence factor and a given driving time. Moreover, we also find that the speed of quantum evolution can be obviously accelerated in the wide range of the ohmicity parameter, i.e., from sub-Ohmic to Ohmic and super-Ohmic cases, which is different from the thermal equilibrium environment case.

关键词: quantum speed limits, non-Markovianity, nonequilibrium environment

Abstract: The speed of evolution of a qubit undergoing a nonequilibrium environment with spectral density of general ohmic form is investigated. First we reveal non-Markovianity of the model, and find that the non-Markovianity quantified by information backflow of Breuer et al. [Phys. Rev. Lett. 103 210401 (2009)] displays a nonmonotonic behavior for different values of the ohmicity parameter s in fixed other parameters and the maximal non-Markovianity can be achieved at a specified value s. We also find that the non-Markovianity displays a nonmonotonic behavior with the change of a phase control parameter. Then we further discuss the relationship between quantum speed limit (QSL) time and non-Markovianity of the open-qubit system for any initial states including pure and mixed states. By investigation, we find that the QSL time of a qubit with any initial states can be expressed by a simple factorization law: the QSL time of a qubit with any qubit-initial states are equal to the product of the coherence of the initial state and the QSL time of maximally coherent states, where the QSL time of the maximally coherent states are jointly determined by the non-Markovianity, decoherence factor and a given driving time. Moreover, we also find that the speed of quantum evolution can be obviously accelerated in the wide range of the ohmicity parameter, i.e., from sub-Ohmic to Ohmic and super-Ohmic cases, which is different from the thermal equilibrium environment case.

Key words: quantum speed limits, non-Markovianity, nonequilibrium environment

中图分类号: (Decoherence; open systems; quantum statistical methods)

03.65.Yz

03.67.Lx (Quantum computation architectures and implementations) 03.67.-a (Quantum information) 42.50.-p (Quantum optics)

贺志, 姚春梅, 李莉, 王琼. Quantum speed limits of a qubit system interacting with a nonequilibrium environment[J]. 中国物理B, 2016, 25(8): 80304-080304.

Zhi He(贺志), Chun-Mei Yao(姚春梅), Li Li(李莉), Qiong Wang(王琼). Quantum speed limits of a qubit system interacting with a nonequilibrium environment[J]. Chin. Phys. B, 2016, 25(8): 80304-080304.

参考文献 57

[1]	Bekenstein J D 1981 Phys. Rev. Lett. 46 623
[2]	Lloyd S 2000 Nature 406 1047
[3]	Yung M H 2006 Phys. Rev. A 74 030303
[4]	Giovanetti V, Lloyd S and Maccone L 2011 Nat. Photon. 5 222
[5]	Alipour S, Mehboudi M and Rezakhani A T 2014 Phys. Rev. Lett. 112 120405
[6]	Caneva T, Murphy M, Calarco T, Fazio R, Montangero S and Giovannetti V and Santoro G E 2009 Phys. Rev. Lett. 103 240501
[7]	Deffner S and Lutz E 2012 Phys. Rev. Lett. 105 170402
[8]	Mandelstam L and Tamm I 1945 J. Phys. (USSR) 9 249
[9]	Margolus N and Levitin L B 1998 Physica D (Amsterdam) 120 188
[10]	Pfeifer P 2008 Phys. Rev. Lett. 70 3365
[11]	Pfeifer P and Frohlich J 1995 Rev. Mod. Phys. 67 759
[12]	Giovannetti V, Lloyd S and Maccone L 2003 Phys. Rev. A 67 052109
[13]	Luo S 2004 Physica D 189 1
[14]	Jones P J and Kok P 2010 Phys. Rev. A 82 022107
[15]	Zwierz M 2012 Phys. Rev. A 86 016101
[16]	Deffner S and Lutz E 2013 J. Phys. A:Math. Theor. 46 335302
[17]	Taddei M M, Escher B M, Davidovich L and de Matos Filho R L 2013 Phys. Rev. Lett. 110 050402
[18]	del Campo A, Egusquiza I L, Plenio M B and Huelga S F 2013 Phys. Rev. Lett. 110 050403
[19]	Deffner S and Lutz E 2013 Phys. Rev. Lett. 111 010402
[20]	Cimmarusti A D, Yan Z, Patterson B D, Corcos L P, Orozco L A and Deffner S 2015 Phys. Rev. Lett. 114 233602
[21]	Zhang Y J, Han W, Xia Y J, Cao J P and Fan H 2014 Sci. Rep. 4 4890
[22]	Sun Z, Liu J, Ma J and Wang X 2015 Sci. Rep. 5 8444
[23]	Xu Z Y 2015 arXiv:1510.00101v2[quant-ph]
[24]	Jing J, Wu L A and del Campo A 2015 arXiv:1510.01106v2[quant-ph]
[25]	Xu Z Y and Zhu S Q 2014 Chin. Phys. Lett. 31 020301
[26]	Xu Z Y, Luo S, Yang W L, Liu C and Zhu S Q 2014 Phys. Rev. A 89 012307
[27]	Zhang Y J, Han W, Xia Y J, Cao J P and Fan H 2015 Phys. Rev. A 91 032112
[28]	Liu C, Xu Z Y and Zhu S Q 2015 Phys. Rev. A 91 022102
[29]	Marvian I and Lidar D A 2015 Phys. Rev. Lett. 115 210402
[30]	Marvian I, Spekkens R W and Zanardi P 2016 Phys. Rev. A 93 052331
[31]	Han W, Jiang K X, Zhang Y J and Xia Y J 2015 Chin. Phys. B 24 120304)
[32]	Liu H B, Yang W L, An J H and Xu Z Y 2016 Phys. Rev. A 93 020105(R)
[33]	Martens C C 2010 J. Chem. Phys. 133 241101
[34]	Marten C C 2012 J. Phys. B:At. Mol. Opt. Phys. 45 154008
[35]	Lombardo F C and Villar P I 2013 Phys. Rev. A 87 032338
[36]	Lombardo F C and Villar P I 2015 Phys. Rev. A 91 042111
[37]	Breuer H P, Laine E M and Piilo J 2009 Phys. Rev. Lett. 103 210401
[38]	Palma G M, Suominen K and Ekert A 1996 Proc. R. Soc. London A 452 567
[39]	Breuer H P and Petruccione F 2002 The Theory of Open Quantum Systems (Oxford:Oxford University Press)
[40]	Goan H S, Jian C C and Chen P W 2010 Phys. Rev. A 82 012111
[41]	Morozov V G, Mathey S and Ropke G 2012 Phys. Rev. A 85 022101
[42]	Haikka P, Johnson T H and Maniscalco S 2013 Phys. Rev. A 87 010103(R)
[43]	Rivas A, Huelga S F and Plenio M B 2010 Phys. Rev. Lett. 105 050403
[44]	Lu X M, Wang X G and Sun C P 2010 Phys. Rev. A 82 042103
[45]	Luo S, Fu S and Song H 2012 Phys. Rev. A 86 044101
[46]	Zeng H S, Tang N, Zheng Y P and Wang G Y 2011 Phys. Rev. A 84 032118
[47]	He Z, Zou J, Li L and Shao B 2011 Phys. Rev. A 83 012108
[48]	Tian L J Ti M M and Zhai X D 2015 Chin. Phys. B 24 100305
[49]	Fan Z L, Ren Y K and Zeng H S 2016 Chin.Phys. B 25 010303
[50]	Nielsen M A and Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge:Cambridge University Press)
[51]	Audenaert K M R 2014 Quantum Inf. Comput. 14 31
[52]	Baumgratz T, Cramer M and Plenio M B 2014 Phys. Rev. Lett. 113 140401
[53]	Baumgratz T, Cramer M and Plenio M B 2014 Phys. Rev. Lett. 113 012108
[54]	Konrad T, de Melo F, Tiersch M, Kasztelan C, Aragão A and Buchleitner A 2008 Nat. Phys. 4 99
[55]	Addis C, Bylicka B, Chruściński D and Maniscalco S 2014 Phys. Rev. A 90 052103
[56]	Addis C, Brebner G, Haikka P and Maniscalco S 2014 Phys. Rev. A 89 024101
[57]	Zhang Y J, Han W, Xia Y J, Yu J M and Fan H 2015 Sci. Rep. 5 13359

Quantum speed limits of a qubit system interacting with a nonequilibrium environment

Quantum speed limits of a qubit system interacting with a nonequilibrium environment

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 57

相关文章 12

Metrics

本文评价

推荐阅读 0

[1]	Jing Zeng(曾静), Yaju Song(宋亚菊), Jing Lu(卢竞), and Lan Zhou(周兰). Non-Markovianity of an atom in a semi-infinite rectangular waveguide[J]. 中国物理B, 2023, 32(3): 30305-030305.
[2]	Zhenyu Lin(林振宇), Tian Liu(刘天), Zongliang Li(李宗良), Yanhui Zhang(张延惠), and Kang Lan(蓝康). Quantum speed limit of the double quantum dot in pure dephasing environment under measurement[J]. 中国物理B, 2022, 31(7): 70307-070307.
[3]	熊飞雷, 杨万里, 冯芒. Generating Kerr nonlinearity with an engineered non-Markovian environment[J]. 中国物理B, 2020, 29(4): 40302-040302.
[4]	Munsif Jan, 许小冶, 王琴琴, 陈哲, 韩永建, 李传锋, 郭光灿. Dipole-dipole interactions enhance non-Markovianity and protect information against dissipation[J]. 中国物理B, 2019, 28(9): 90303-090303.
[5]	李逊, 熊标, 晁石磊, 金家森, 周玲. Dynamics of two levitated nanospheres nonlinearly coupling with non-Markovian environment[J]. 中国物理B, 2019, 28(5): 50302-050302.
[6]	徐凯, 韩伟, 张英杰, 范桁. Non-Markovian speedup dynamics control of the damped Jaynes-Cummings model with detuning[J]. 中国物理B, 2018, 27(1): 10302-010302.
[7]	范子龙, 任玉坤, 曾浩生. Entanglement and non-Markovianity of a multi-level atom decaying in a cavity[J]. 中国物理B, 2016, 25(1): 10303-010303.
[8]	王国友, 唐宁, 刘颖, 曾浩生. Rotation of Bloch sphere induced by Lamb shift in open two-level systems[J]. 中国物理B, 2015, 24(5): 50302-050302.
[9]	田立君, 提敏敏, 翟向东. Non-Markovianity of a qubit coupled with an isotropic Lipkin-Meshkov-Glick bath[J]. 中国物理B, 2015, 24(10): 100305-100305.
[10]	范子龙, 田晶, 曾浩生. Entanglement and non-Markovianity of a spin-S system in a dephasing environment[J]. 中国物理B, 2014, 23(6): 60303-060303.
[11]	唐宁, 徐甜甜, 曾浩生. Comparison between non-Markovian dynamics with and without rotating wave approximation[J]. 中国物理B, 2013, 22(3): 30304-030304.
[12]	郑艳萍, 唐宁, 王国友, 曾浩生. Distribution of non-Markovian intervals for open qubit systems[J]. 中国物理B, 2011, 20(11): 110301-110301.