与XY双自旋链耦合的双量子比特系统的关联性与相干性

杨阳; 王安民; 曹连振; 赵加强; 逯怀新

doi:10.7498/aps.67.20180812

摘要

研究了双量子比特系统中在具有Dzyaloshinsky-Moriya相互作用的独立XY自旋链环境下的相干性与关联性动力学.推导出相干性与关联性的演化规律.发现在自旋链的临界点附近，当tt0时，系统相干性的演化与经典关联完全相同；而在tt0时，则与量子关联完全相同；在t0时刻，量子关联突变为经典关联.

关键词:

Quantum coherence has played a decisive role in quantum information processing. On the other hand, quantum correlation can be considered as a powerful resource for delivering quantum information. Both quantum coherence and quantum correlation may occur in an information propagating process, which challenges us to understand the relationship between coherence and correlation. This is also an important procedure for physicists to know the features of quantum resources. Any quantum system interacting with its surrounding environment will destroy the quantum coherence and fail to fulfil any task of delivering quantum information. In this sense, studying the dynamics of quantum correlation and quantum coherence is very fascinating. In this paper, we investigate the dynamics of the quantum correlation and quantum coherence for two central qubits coupled to their own spin baths modeled by the XY spin chain with Dzyaloshinsky-Moriya interaction. We employ the quantum discord to characterize the quantum correlation, and use the relative entropy to measure quantum coherence. In this way the evolution law of the quantum discord and the relative entropy of quantum coherence of two-qubit system are derived, and the evolution law depends not only on the Dzyaloshinsky-Moriya interaction, the anisotropy parameter and the total number of spin chain sites, but also on the coupling strength between the central spin and its spin chain. Our findings are as follows. Firstly, we find that near the critical point of spin chain the quantum coherence abruptly changes, which can be used to detect the existence of quantum phase transition. Secondly, at the critical point, the relative entropy of quantum coherence is the same as that of classical correlation when time tt0, and it is the same as that of quantum discord when time tt0. At time t0, the sudden transition from quantum discord to classical correlation occurs. All in all, the relative entropy of quantum coherence reflects the behaviors of classical correlation and quantum discord for times tt0 and tt0, respectively, which is caused by the change of the optimal basis for quantum discord. Thirdly, the dynamics of quantum correlation and quantum coherence keep invariant under the scaling variation of the total number of spin chain sites and the coupling strength. Moreover, we find that all the Dzyaloshinsky-Moriya interactions and the anisotropy parameters, as well as the coupling strengths will enhance the decay of quantum coherence and quantum correlation, while they have no obvious effect on the relationship between dynamics of coherence and correlation. The above discussion reveals some new features of quantum coherence and quantum correlation, which may be useful in further developing quantum information theory.

Keywords:

作者及机构信息

1.
潍坊学院物理与光电工程学院, 山东省多光子纠缠与操纵实验室, 潍坊 261061;

2.
中国科学技术大学近代物理系, 合肥 230026

通信作者: 杨阳, yangyang@mail.ustc.edu.cn

基金项目: 国家自然科学基金（批准号：11404246）和山东省自然科学基金（批准号：ZR2017MF040）资助的课题.

Authors and contacts

1.
Shandong Provincial Key Laboratory of Multi-Photon Entanglement and Manipulation, Department of Physics and Optoelectronic Engineering, Weifang University, Weifang 261061, China;

2.
Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China

Corresponding author: Yang Yang, yangyang@mail.ustc.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11404246) and the Shandong Provincial Natural Science Foundation, China (Grant No. ZR2017MF040).

参考文献

[1]	Asbth J K, Calsamiglia J, Ritsch H 2005 Phys. Rev. Lett. 94 173602
[2]	Streltsov A, Singh U, Dhar H S, Bera M N, Adesso G 2015 Phys. Rev. Lett. 115 020403
[3]	Giovannetti V, Lloyd S, Maccone L 2011 Nat. Photon. 5 222
[4]	Xiang G Y, Guo G C 2013 Chin. Phys. B 22 110601
[5]	Dobrznski R D, Maccone L 2014 Phys. Rev. Lett. 113 250801
[6]	Correa L A, Palao J P, Alonso D, Adesso G 2014 Sci. Rep. 4 3949
[7]	Rnagel J, Abah O, Schmidt-Kaler F, Singer K, Lutz E 2014 Phys. Rev. Lett. 112 030602
[8]	Lostaglio M, Jennings D, Rudolph T 2015 Nat. Commun. 6 6383
[9]	Plenio M B, Huelga S F 2008 New J. Phys. 10 113019
[10]	Li C M, Lambert N, Chen Y N, Chen G Y, Nori F 2012 Sci. Rep. 2 885
[11]	Huelga S F, Plenio M B 2013 Contemp. Phys. 54 181
[12]	Baumgratz T, Cramer M, Plenio M B 2014 Phys. Rev. Lett. 113 140401
[13]	Yuan X, Zhou H, Cao Z, Ma X 2015 Phys. Rev. A 92 022124
[14]	Du S, Bai Z, Qi X 2015 Quantum Inf. Comput. 15 1307
[15]	Winter A, Yang D 2016 Phys. Rev. Lett. 116 120404
[16]	Chitambar E, Streltsov A, Rana S, Bera M N, Adesso G, Lewenstein M 2016 Phys. Rev. Lett. 116 070402
[17]	Chitambar E, Hsieh M H 2016 Phys. Rev. Lett. 117 020402
[18]	Girolami D, Yadin B 2017 Entropy 19 124
[19]	Datta A, Shaji A, Caves C M 2008 Phys. Rev. Lett. 100 050502
[20]	Lanyon B P, Barbieri M, Almeida M P, White A G 2008 Phys. Rev. Lett. 101 200501
[21]	Dakić B, Lipp Y O, Ma X S, Ringbauer M, Kropatschek S, Barz S, Paterek T, Vedral V, Zeilinger A, Brukner C, Walther P 2012 Nat. Phys. 8 666
[22]	Ma J, Yadin B, Girolami D, Vedral V, Gu M 2016 Phys. Rev. Lett. 116 160407
[23]	Maziero J, Guzman H C, Ćeleri L C, Sarandy M S, Serra R 2010 Phys. Rev. A 82 012106
[24]	Sun Y, Mao Y Y, Luo S L 2017 Europhys. Lett. 118 60007
[25]	Hou J X, Liu S Y, Wang X H, Yang W L 2017 Phys. Rev. A 96 042324
[26]	Fanchini F F, Werlang T, Brasil C A, ArrudaL G E, Caldeira A O 2010 Phys. Rev. A 81 052107
[27]	Mazzola L, Piilo J, Maniscalco S 2010 Phys. Rev. Lett. 104 200401
[28]	Hu Z D, Wang J C, Zhang Y X, Zhang Y Q 2014 J. Phys. Soc. Jpn. 83 114004
[29]	Hu Z D, Zhang Y X, Zhang Y Q 2014 Quantum Inf. Process. 13 1841
[30]	Xu J S, Xu X Y, Li C F, Zhang C J, Zou X B, Guo G C 2010 Nat. Commun. 1 7
[31]	Luo D W, Lin H Q, Xu J B, Yao D X 2011 Phys. Rev. A 84 062112
[32]	Li Y C, Lin H Q, Xu J B 2012 Europhys. Lett. 100 20002
[33]	Yang Y, Wang A M 2014 Chin. Phys. B 23 020307
[34]	Yang Y, Wang A M 2013 Acta Phys. Sin. 62 130305 (in Chinese) [杨阳, 王安民 2013 62 130305]
[35]	Bromley T R, Cianciaruso M, Adesso G 2015 Phys. Rev. Lett. 114 210401
[36]	Yu X D, Zhang D J, Liu C L, Tong D M 2016 Phys. Rev. A 93 060303
[37]	Hu M L, Fan H 2017 Phys. Rev. A 95 052106
[38]	Hu M L, Shen S Q, Fan H 2017 Phys. Rev. A 96 052309
[39]	Silva I A, Souza A M, Bromley T R, Cianciaruso M, Marx R, Sarthour R S, Oliveira R S, Franco R L, Glaser S J, de Azevedo E R, Soares-Pinto D O, Adesso G 2016 Phys. Rev. Lett. 117 160402
[40]	Hu M L, Fan H 2016 Sci. Rep. 6 29260
[41]	Yang L W, Xia Y J 2016 Chin. Phys. B 25 110303
[42]	Yang L W, Han W, Xia Y J 2018 Chin. Phys. B 27 040302
[43]	Zhao M J, Ma T, Ma Y Q 2018 Sci. China: Phys. Mech. Astron. 61 020311
[44]	Gao D Y, Gao Q, Xia Y J 2017 Chin. Phys. B 26 110303
[45]	Qiu L, Wang A M 2011 Phys. Scr. 84 045021
[46]	Cheng W W, Liu J M 2009 Phys. Rev. A 79 052320
[47]	Hu M L, Fan H 2010 Phys. Lett. A 374 3520
[48]	Ollivier H, Zurek W H 2001 Phys. Rev. Lett. 88 017901
[49]	Hu Z D, Wei M S, Wang J C, Zhang Y X, He Q L 2018 J. Phys. Soc. Jpn. 87 054002

施引文献

[1]	Asbth J K, Calsamiglia J, Ritsch H 2005 Phys. Rev. Lett. 94 173602
[2]	Streltsov A, Singh U, Dhar H S, Bera M N, Adesso G 2015 Phys. Rev. Lett. 115 020403
[3]	Giovannetti V, Lloyd S, Maccone L 2011 Nat. Photon. 5 222
[4]	Xiang G Y, Guo G C 2013 Chin. Phys. B 22 110601
[5]	Dobrznski R D, Maccone L 2014 Phys. Rev. Lett. 113 250801
[6]	Correa L A, Palao J P, Alonso D, Adesso G 2014 Sci. Rep. 4 3949
[7]	Rnagel J, Abah O, Schmidt-Kaler F, Singer K, Lutz E 2014 Phys. Rev. Lett. 112 030602
[8]	Lostaglio M, Jennings D, Rudolph T 2015 Nat. Commun. 6 6383
[9]	Plenio M B, Huelga S F 2008 New J. Phys. 10 113019
[10]	Li C M, Lambert N, Chen Y N, Chen G Y, Nori F 2012 Sci. Rep. 2 885
[11]	Huelga S F, Plenio M B 2013 Contemp. Phys. 54 181
[12]	Baumgratz T, Cramer M, Plenio M B 2014 Phys. Rev. Lett. 113 140401
[13]	Yuan X, Zhou H, Cao Z, Ma X 2015 Phys. Rev. A 92 022124
[14]	Du S, Bai Z, Qi X 2015 Quantum Inf. Comput. 15 1307
[15]	Winter A, Yang D 2016 Phys. Rev. Lett. 116 120404
[16]	Chitambar E, Streltsov A, Rana S, Bera M N, Adesso G, Lewenstein M 2016 Phys. Rev. Lett. 116 070402
[17]	Chitambar E, Hsieh M H 2016 Phys. Rev. Lett. 117 020402
[18]	Girolami D, Yadin B 2017 Entropy 19 124
[19]	Datta A, Shaji A, Caves C M 2008 Phys. Rev. Lett. 100 050502
[20]	Lanyon B P, Barbieri M, Almeida M P, White A G 2008 Phys. Rev. Lett. 101 200501
[21]	Dakić B, Lipp Y O, Ma X S, Ringbauer M, Kropatschek S, Barz S, Paterek T, Vedral V, Zeilinger A, Brukner C, Walther P 2012 Nat. Phys. 8 666
[22]	Ma J, Yadin B, Girolami D, Vedral V, Gu M 2016 Phys. Rev. Lett. 116 160407
[23]	Maziero J, Guzman H C, Ćeleri L C, Sarandy M S, Serra R 2010 Phys. Rev. A 82 012106
[24]	Sun Y, Mao Y Y, Luo S L 2017 Europhys. Lett. 118 60007
[25]	Hou J X, Liu S Y, Wang X H, Yang W L 2017 Phys. Rev. A 96 042324
[26]	Fanchini F F, Werlang T, Brasil C A, ArrudaL G E, Caldeira A O 2010 Phys. Rev. A 81 052107
[27]	Mazzola L, Piilo J, Maniscalco S 2010 Phys. Rev. Lett. 104 200401
[28]	Hu Z D, Wang J C, Zhang Y X, Zhang Y Q 2014 J. Phys. Soc. Jpn. 83 114004
[29]	Hu Z D, Zhang Y X, Zhang Y Q 2014 Quantum Inf. Process. 13 1841
[30]	Xu J S, Xu X Y, Li C F, Zhang C J, Zou X B, Guo G C 2010 Nat. Commun. 1 7
[31]	Luo D W, Lin H Q, Xu J B, Yao D X 2011 Phys. Rev. A 84 062112
[32]	Li Y C, Lin H Q, Xu J B 2012 Europhys. Lett. 100 20002
[33]	Yang Y, Wang A M 2014 Chin. Phys. B 23 020307
[34]	Yang Y, Wang A M 2013 Acta Phys. Sin. 62 130305 (in Chinese) [杨阳, 王安民 2013 62 130305]
[35]	Bromley T R, Cianciaruso M, Adesso G 2015 Phys. Rev. Lett. 114 210401
[36]	Yu X D, Zhang D J, Liu C L, Tong D M 2016 Phys. Rev. A 93 060303
[37]	Hu M L, Fan H 2017 Phys. Rev. A 95 052106
[38]	Hu M L, Shen S Q, Fan H 2017 Phys. Rev. A 96 052309
[39]	Silva I A, Souza A M, Bromley T R, Cianciaruso M, Marx R, Sarthour R S, Oliveira R S, Franco R L, Glaser S J, de Azevedo E R, Soares-Pinto D O, Adesso G 2016 Phys. Rev. Lett. 117 160402
[40]	Hu M L, Fan H 2016 Sci. Rep. 6 29260
[41]	Yang L W, Xia Y J 2016 Chin. Phys. B 25 110303
[42]	Yang L W, Han W, Xia Y J 2018 Chin. Phys. B 27 040302
[43]	Zhao M J, Ma T, Ma Y Q 2018 Sci. China: Phys. Mech. Astron. 61 020311
[44]	Gao D Y, Gao Q, Xia Y J 2017 Chin. Phys. B 26 110303
[45]	Qiu L, Wang A M 2011 Phys. Scr. 84 045021
[46]	Cheng W W, Liu J M 2009 Phys. Rev. A 79 052320
[47]	Hu M L, Fan H 2010 Phys. Lett. A 374 3520
[48]	Ollivier H, Zurek W H 2001 Phys. Rev. Lett. 88 017901
[49]	Hu Z D, Wei M S, Wang J C, Zhang Y X, He Q L 2018 J. Phys. Soc. Jpn. 87 054002

[1]	胡飞飞, 李思莹, 朱顺, 黄昱, 林旭斌, 张思拓, 范云茹, 周强, 刘云. 用于量子纠缠密钥的多波长对量子关联光子对产生. , 2024, 73(23): 230304. doi: 10.7498/aps.73.20241274
[2]	余敏, 郭有能. 关联退相位有色噪声通道下熵不确定关系的调控. , 2024, 73(22): 220301. doi: 10.7498/aps.73.20241171
[3]	尹伊. 强相互作用物质中的自旋与运动关联. , 2023, 72(11): 111201. doi: 10.7498/aps.72.20222458
[4]	李丽娟, 明飞, 宋学科, 叶柳, 王栋. 熵不确定度关系综述. , 2022, 71(7): 070302. doi: 10.7498/aps.71.20212197
[5]	张诗豪, 张向东, 李绿周. 基于测量的量子计算研究进展. , 2021, 70(21): 210301. doi: 10.7498/aps.70.20210923
[6]	陈爱民, 刘东昌, 段佳, 王洪雷, 相春环, 苏耀恒. 含有Dzyaloshinskii-Moriya相互作用的自旋1键交替海森伯模型的量子相变和拓扑序标度. , 2020, 69(9): 090302. doi: 10.7498/aps.69.20191773
[7]	贺志, 余敏, 王琼. 多格点相互作用对横向磁场作用下XY型自旋链中非平衡态热力学性质的影响. , 2019, 68(24): 240506. doi: 10.7498/aps.68.20190525
[8]	伊天成, 丁悦然, 任杰, 王艺敏, 尤文龙. 具有Dzyaloshinskii-Moriya相互作用的XY模型的量子相干性. , 2018, 67(14): 140303. doi: 10.7498/aps.67.20172755
[9]	李小影, 黄灿, 朱岩, 李晋斌, 樊济宇, 潘燕飞, 施大宁, 马春兰. -(Zn,Cr)S(111)表面上的Dzyaloshinsky-Moriya作用:第一性原理计算. , 2018, 67(13): 137101. doi: 10.7498/aps.67.20180342
[10]	黄灿, 李小影, 朱岩, 潘燕飞, 樊济宇, 施大宁, 马春兰. 第一性原理计算Co/h-BN界面上的微弱Dzyaloshinsky-Moriya相互作用. , 2018, 67(11): 117102. doi: 10.7498/aps.67.20180337
[11]	丛美艳, 杨晶, 黄燕霞. 在不同初态下Dzyaloshinskii-Moriya相互作用及内禀退相干对海森伯系统的量子纠缠的影响. , 2016, 65(17): 170301. doi: 10.7498/aps.65.170301
[12]	邹琴, 胡小勉, 刘金明. Dzyaloshinskii-Moriya相互作用和内禀消相干对基于两量子比特Heisenberg自旋系统的量子密集编码的影响. , 2015, 64(8): 080302. doi: 10.7498/aps.64.080302
[13]	秦猛, 李延标, 白忠. 非均匀磁场和杂质磁场对自旋1系统量子关联的影响. , 2015, 64(3): 030301. doi: 10.7498/aps.64.030301
[14]	秦猛, 李延标, 白忠, 王晓. 不同方向Dzyaloshinskii-Moriya相互作用和磁场对自旋系统纠缠和保真度退相干的影响. , 2014, 63(11): 110302. doi: 10.7498/aps.63.110302
[15]	樊开明, 张国锋. 阻尼Jaynes-Cummings模型中两原子的量子关联动力学. , 2013, 62(13): 130301. doi: 10.7498/aps.62.130301
[16]	谢美秋, 郭斌. 不同磁场环境下Heisenberg XXZ自旋链中的热量子失协. , 2013, 62(11): 110303. doi: 10.7498/aps.62.110303
[17]	杨阳, 王安民. 与Ising链耦合的中心双量子比特系统的量子关联. , 2013, 62(13): 130305. doi: 10.7498/aps.62.130305
[18]	单传家. 具有三体相互作用的自旋链系统中的几何相位与量子相变. , 2012, 61(22): 220302. doi: 10.7498/aps.61.220302
[19]	刘圣鑫, 李莎莎, 孔祥木. Dzyaloshinskii-Moriya相互作用对量子XY链中热纠缠的影响. , 2011, 60(3): 030303. doi: 10.7498/aps.60.030303
[20]	单传家, 程维文, 刘堂昆, 黄燕霞, 李宏. 具有Dzyaloshinskii-Moriya相互作用的一维随机量子XY模型中的纠缠特性. , 2008, 57(5): 2687-2694. doi: 10.7498/aps.57.2687

计量

文章访问数: 6859
PDF下载量: 225
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板