Correlation and coherence for two-qubit system coupled to XY spin chains

Yang Yang; Wang An-Min; Cao Lian-Zhen; Zhao Jia-Qiang; Lu Huai-Xin

doi:10.7498/aps.67.20180812

Abstract

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:

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).

References

[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

Cited By

[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]	Hu Fei-Fei, Li Si-Ying, Zhu Shun, Huang Yu, Lin Xu-Bin, Zhang Si-Tuo, Fan Yun-Ru, Zhou Qiang, Liu Yun. Generation of multiwavelength quantum correlated photon pair for quantum entanglement key distribution. Acta Physica Sinica, 2024, 73(23): 230304. doi: 10.7498/aps.73.20241274
[2]	Yu Min, Guo You-Neng. Regulation of entropic uncertainty relation in correlated channels with dephasing colored noise. Acta Physica Sinica, 2024, 73(22): 220301. doi: 10.7498/aps.73.20241171
[3]	Yin Yi. Quantum correlation between spin and motion in quantum chromodynamics matter. Acta Physica Sinica, 2023, 72(11): 111201. doi: 10.7498/aps.72.20222458
[4]	Li Li-Juan, Ming Fei, Song Xue-Ke, Ye Liu, Wang Dong. Review on entropic uncertainty relations. Acta Physica Sinica, 2022, 71(7): 070302. doi: 10.7498/aps.71.20212197
[5]	Zhang Shi-Hao, Zhang Xiang-Dong, Li Lü-Zhou. Research progress of measurement-based quantum computation. Acta Physica Sinica, 2021, 70(21): 210301. doi: 10.7498/aps.70.20210923
[6]	Chen Ai-Min, Liu Dong-Chang, Duan Jia, Wang Hong-Lei, Xiang Chun-Huan, Su Yao-Heng. Quantum phase transition and topological order scaling in spin-1 bond-alternating Heisenberg model with Dzyaloshinskii-Moriya interaction. Acta Physica Sinica, 2020, 69(9): 090302. doi: 10.7498/aps.69.20191773
[7]	He Zhi, Yu Min, Wang Qiong. Effects of multisite interaction on nonequilibrium thermodynamics of XY spin chain in a transverse filed. Acta Physica Sinica, 2019, 68(24): 240506. doi: 10.7498/aps.68.20190525
[8]	Yi Tian-Cheng, Ding Yue-Ran, Ren Jie, Wang Yi-Min, You Wen-Long. Quantum coherence of XY model with Dzyaloshinskii-Moriya interaction. Acta Physica Sinica, 2018, 67(14): 140303. doi: 10.7498/aps.67.20172755
[9]	Li Xiao-Ying, Huang Can, Zhu Yan, Li Jin-Bin, Fan Ji-Yu, Pan Yan-Fei, Shi Da-Ning, Ma Chun-Lan. Dzyaloshinsky-Moriya interaction in -(Zn, Cr)S(111) surface: First principle calculations. Acta Physica Sinica, 2018, 67(13): 137101. doi: 10.7498/aps.67.20180342
[10]	Huang Can, Li Xiao-Ying, Zhu Yan, Pan Yan-Fei, Fan Ji-Yu, Shi Da-Ning, Ma Chun-Lan. First principle study of weak Dzyaloshinsky-Moriya interaction in Co/BN surface. Acta Physica Sinica, 2018, 67(11): 117102. doi: 10.7498/aps.67.20180337
[11]	Cong Mei-Yan, Yang Jing, Huang Yan-Xia. Effects of Dzyaloshinskii-Moriya interacton and decoherence on entanglement dynamics in Heisenberg spin chain system with different initial states. Acta Physica Sinica, 2016, 65(17): 170301. doi: 10.7498/aps.65.170301
[12]	Zou Qin, Hu Xiao-Mian, Liu Jin-Ming. Effects of Dzyaloshinskii-Moriya interaction and intrinsic decoherence on quantum dense coding via a two-qubit Heisenberg spin system. Acta Physica Sinica, 2015, 64(8): 080302. doi: 10.7498/aps.64.080302
[13]	Qin Meng, Li Yan-Biao, Bai Zhong. Effects of inhomogeneous magnetic field and magnetic impurity on the quantum correlation of spin-1 system. Acta Physica Sinica, 2015, 64(3): 030301. doi: 10.7498/aps.64.030301
[14]	Qin Meng, Li Yan-Biao, Bai Zhong, Wang Xiao. Effects of different Dzyaloshinskii-Moriya interaction and magnetic field on entanglement and fidelity intrinsic decoherence in a spin system. Acta Physica Sinica, 2014, 63(11): 110302. doi: 10.7498/aps.63.110302
[15]	Fan Kai-Ming, Zhang Guo-Feng. The dynamics of quantum correlation between two atoms in a damping Jaynes-Cummings model. Acta Physica Sinica, 2013, 62(13): 130301. doi: 10.7498/aps.62.130301
[16]	Xie Mei-Qiu, Guo Bin. Thermal quantum discord in Heisenberg XXZ model under different magnetic field conditions. Acta Physica Sinica, 2013, 62(11): 110303. doi: 10.7498/aps.62.110303
[17]	Yang Yang, Wang An-Min. Quantum correlation for a central two-qubit system coupled to Ising chain. Acta Physica Sinica, 2013, 62(13): 130305. doi: 10.7498/aps.62.130305
[18]	Shan Chuan-Jia. Berry phase and quantum phase transition in spin chain system with three-site interaction. Acta Physica Sinica, 2012, 61(22): 220302. doi: 10.7498/aps.61.220302
[19]	Liu Sheng-Xin, Li Sha-Sha, Kong Xiang-Mu. The effect of Dzyaloshinskii-Moriya interaction on entanglement in one-dimensional XY spin model. Acta Physica Sinica, 2011, 60(3): 030303. doi: 10.7498/aps.60.030303
[20]	Shan Chuan-Jia, Cheng Wei-Wen, Liu Tang-Kun, Huang Yan-Xia, Li Hong. The entanglement in one-dimensional random XY spin chain with Dzyaloshinskii-Moriya interaction. Acta Physica Sinica, 2008, 57(5): 2687-2694. doi: 10.7498/aps.57.2687

Catalog

Vol. 67, Issue 15 - 2018-08-05

Metrics

Abstract views: 6861
PDF Downloads: 225
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板