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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

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
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  • 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.
      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).
    [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 物理学报 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]

    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 物理学报 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

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  • Received Date:  25 April 2018
  • Accepted Date:  20 May 2018
  • Published Online:  05 August 2018

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

    Corresponding author: Yang Yang, yangyang@mail.ustc.edu.cn
  • 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
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 11404246) and the Shandong Provincial Natural Science Foundation, China (Grant No. ZR2017MF040).

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.

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