One-way quantum deficit and quantum coherence in the anisotropic XY chain

  • Biao-Liang Ye
  • Bo LiEmail author
  • Li-Jun Zhao
  • Hai-Jun Zhang
  • Shao-Ming FeiEmail author


In this study, we investigate pairwise non-classical correlations measured using a one-way quantum deficit as well as quantum coherence in the XY spin-1/2 chain in a transverse magnetic field for both zero and finite temperatures. The analytical and numerical results of our investigations are presented. In the case when the temperature is zero, it is shown that the one-way quantum deficit can characterize quantum phase transitions as well as quantum coherence. We find that these measures have a clear critical point at λ = 1. When λ ≤ 1, the one-way quantum deficit has an analytical expression that coincides with the relative entropy of coherence. We also study an XX model and an Ising chain at the finite temperatures.


one-way quantum deficit quantum coherence quantum phase transitions XY chain 

PACS number(s)

03.67.-a 73.43.Nq 75.10.Pq 


  1. 1.
    L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Rev. Mod. Phys. 80, 517 (2008).ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys. 81, 865 (2009).ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    T. Monz, P. Schindler, J. T. Barreiro, M. Chwalla, D. Nigg, W. A. Coish, M. Harlander, W. Hänsel, M. Hennrich, and R. Blatt, Phys. Rev. Lett. 106, 130506 (2011).ADSCrossRefGoogle Scholar
  4. 4.
    R. Barends, J. Kelly, A. Megrant, A. Veitia, D. Sank, E. Jeffrey, T. C. White, J. Mutus, A. G. Fowler, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, C. Neill, P. O’Malley, P. Roushan, A. Vainsencher, J. Wenner, A. N. Korotkov, A. N. Cleland, and J. M. Martinis, Nature 508, 500 (2014).ADSCrossRefGoogle Scholar
  5. 5.
    Q. Lin, Sci. China-Phys. Mech. Astron. 58, 044201 (2015).ADSGoogle Scholar
  6. 6.
    R. Heilmann, M. Gräfe, S. Nolte, and A. Szameit, Sci. Bull. 60, 96 (2015).CrossRefGoogle Scholar
  7. 7.
    X. L. Wang, L. K. Chen, W. Li, H. L. Huang, C. Liu, C. Chen, Y. H. Luo, Z. E. Su, D. Wu, Z. D. Li, H. Lu, Y. Hu, X. Jiang, C. Z. Peng, L. Li, N. L. Liu, Y. A. Chen, C. Y. Lu, and J. W. Pan, Phys. Rev. Lett. 117, 210502 (2016).ADSCrossRefGoogle Scholar
  8. 8.
    A. K. Ekert, Phys. Rev. Lett. 67, 661 (1991).ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    C. H. Bennett, and S. J. Wiesner, Phys. Rev. Lett. 69, 2881 (1992).ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    X. F. Zou, and D. W. Qiu, Sci. China-Phys. Mech. Astron. 57, 1696 (2014).ADSCrossRefGoogle Scholar
  11. 11.
    D. Y. Cao, B. H. Liu, Z. Wang, Y. F. Huang, C. F. Li, and G. C. Guo, Sci. Bull. 60, 1128 (2015).CrossRefGoogle Scholar
  12. 12.
    K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, Rev. Mod. Phys. 84, 1655 (2012).ADSCrossRefGoogle Scholar
  13. 13.
    H. Ollivier, and W. H. Zurek, Phys. Rev. Lett. 88, 017901 (2001).ADSCrossRefGoogle Scholar
  14. 14.
    L. Henderson, and V. Vedral, J. Phys. A-Math. Gen. 34, 6899 (2001).ADSCrossRefGoogle Scholar
  15. 15.
    J. Oppenheim, M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. 89, 180402 (2002).ADSCrossRefGoogle Scholar
  16. 16.
    S. Luo, Phys. Rev. A 77, 022301 (2008).ADSCrossRefGoogle Scholar
  17. 17.
    B. Dakić, V. Vedral, Phys. Rev. Lett. 105, 190502 (2010).ADSCrossRefGoogle Scholar
  18. 18.
    K. Modi, T. Paterek, W. Son, V. Vedral, and M. Williamson, Phys. Rev. Lett. 104, 080501 (2010).ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    S. Luo, and S. Fu, Phys. Rev. Lett. 106, 120401 (2011).ADSCrossRefGoogle Scholar
  20. 20.
    A. Streltsov, G. Adesso, and M. B. Plenio, arXiv: 1609.02439.Google Scholar
  21. 21.
    T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014).ADSCrossRefGoogle Scholar
  22. 22.
    G. Adesso, T. R. Bromley, and M. Cianciaruso, arXiv: 1605.00806.Google Scholar
  23. 23.
    T. J. Osborne, and M. A. Nielsen, Phys. Rev. A 66, 032110 (2002).ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    S. M. Giampaolo, and B. C. Hiesmayr, Phys. Rev. A 88, 052305 (2013).ADSCrossRefGoogle Scholar
  25. 25.
    M. Hofmann, A. Osterloh, and O. Gühne, Phys. Rev. B 89, 134101 (2014).ADSCrossRefGoogle Scholar
  26. 26.
    J. Maziero, H. C. Guzman, L. C. Céleri, M. S. Sarandy, and R. M. Serra, Phys. Rev. A 82, 012106 (2010).ADSCrossRefGoogle Scholar
  27. 27.
    B. Cakmak, G. Karpat, and F. Fanchini, Entropy 17, 790 (2015).ADSCrossRefGoogle Scholar
  28. 28.
    W. W. Cheng, C. J. Shan, Y. B. Sheng, L. Y. Gong, S. M. Zhao, and B. Y. Zheng, Phys. E-Low-Dim. Syst. Nanostr. 44, 1320 (2012).ADSCrossRefGoogle Scholar
  29. 29.
    F. Altintas, and R. Eryigit, Ann. Phys. 327, 3084 (2012).ADSCrossRefGoogle Scholar
  30. 30.
    B. Q. Liu, B. Shao, J. G. Li, J. Zou, and L. A. Wu, Phys. Rev. A 83, 052112 (2011).ADSCrossRefGoogle Scholar
  31. 31.
    A. Streltsov, H. Kampermann, and D. Bruß, Phys. Rev. Lett. 106, 160401 (2011).ADSCrossRefGoogle Scholar
  32. 32.
    E. Barouch, and B. M. McCoy, Phys. Rev. A. 3, 786 (1971).ADSCrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of Physics and Electronic InformationShangrao Normal UniversityShangraoChina
  2. 2.School of Mathematics & Computer ScienceShangrao Normal UniversityShangraoChina
  3. 3.School of Mathematical SciencesCapital Normal UniversityBeijingChina
  4. 4.Max-Planck-Institute for Mathematics in the SciencesLeipzigGermany

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