International Journal of Theoretical Physics

, Volume 55, Issue 2, pp 911–919 | Cite as

Dynamics of Measurement-Induced Non-Locality and Geometric Measure of Discord in a Two-Qubit Heisenberg XY Chain



By taking into account the Dzyaloshinsky-Moriya (DM) interaction under uniform magnetic field, quantum correlation behaviors measured by the measurement-induced nonlocality (MIN) and the geometric measure of discord (GMOD) in a two-qubit XY model are investigated in detail. Turning the different parameters can lead the two kinds of measurements to present different properties. For example, increasing the parameter B(uniform magnetic field), the existing region of MIN is larger than GMOD; MIN can appear the phenomenon of monotonous reduction when the parameter D(Dzyaloshinsky-Moriya interaction) is smaller than one threshold value, while GMOD cannot; MIN monotonously reduces with enhancive value of T(temperature), while GMOD initial experiences a slightly increasing and then decreases. One interesting point is that the more obvious and complicated difference between them are shown from the initial values. This property is both true for the zero temperature and the finite temperature. Through analyzing the limit case of the temperature approaching zero, the analytic solutions give the detailed reasons why have different effect on the initial values. Moreover, from the analytic solutions, we know the initial value of MIN is always larger than or equal to GMOD.


Quantum correlation Measurement-induced nonlocality Geometric measure of discord 



This project was supported by the Natural Science Foundation for Young Scientists of Shanxi Province, China (Grant No. 2012021003-3) and the Special Funds of the National Natural Science Foundation of China (Grant No. 11447207).


  1. 1.
    Luo, S.: Phys. Rev. A 77, 022301 (2008)ADSCrossRefGoogle Scholar
  2. 2.
    Bennett, C.H., DiVincenzo, D.P., Fuchs, C.A., Mor, T., Rains, E., Shor, P.W., Smolin, J.A., Wootters, W.K.: Phys. Rev. A 59, 1070 (1999)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Bell, J.S.: Physics (NY) 1, 195 (1964)Google Scholar
  4. 4.
    Werner, R.F., Wolf, M.M.: Quantum Inf. Comput. 1, 1 (2001)MATHMathSciNetGoogle Scholar
  5. 5.
    Jones, S.J., Wiseman, H.M., Doherty, A.C.: Phys. Rev. A 76, 052116 (2007)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Rev. Mod. Phys. 81, 865 (2009)ADSMATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Augusiak, R., Cavalcanti, D., Prettico, G., Acin, A.: Phys. Rev. Lett. 104, 230401 (2010)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    Piani, M., Horodecki, P., Horodecki, R.: Phys. Rev. Lett. 100, 090502 (2008)ADSCrossRefGoogle Scholar
  9. 9.
    Luo, S., Zhang, Q.: J. Stat. Phys. 131, 1169 (2008)ADSMATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Li, N., Luo, S.: Phys. Rev. A 78, 024303 (2008)ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    Ollivier, H., Zurek, W.H.: Phys. Rev. Lett. 88, 017901 (2001)ADSCrossRefGoogle Scholar
  12. 12.
    Datta, A., Shaji, A., Caves, C.M.: Phys. Rev. Lett. 105, 050502 (2008)CrossRefGoogle Scholar
  13. 13.
    Luo, S., Fu, S.: Phys. Rev. Lett. 106, 120401 (2011)ADSCrossRefGoogle Scholar
  14. 14.
    Dakic, B., Vedral, V., Brukner, C.: Phys. Rev. Lett. 105, 190502 (2010)Google Scholar
  15. 15.
    Luo, S., Fu, S.: Phys. Rev. A 82, 034302 (2010)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    Wiseman, H.M., Jones, S.J., Doherty, A.C.: Phys. Rev. Lett. 98, 140402 (2007)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    Bennett, C.H., DiVicenzo, D.P., Shor, P.W., Smolin, J.A., Rerhal, B.M., Wootters, W.K.: Phys. Rev. Lett. 87, 077902 (2001)ADSCrossRefGoogle Scholar
  18. 18.
    Peter, N.A., Barreiro, J.T., Goggin, M.E., Wei, T.C., Kwiat, P.G.: Phys. Rev. Lett. 94, 150502 (2005)ADSCrossRefGoogle Scholar
  19. 19.
    Mattle, K., Weinfurter, H., Kwiat, P.G., Zeilinger, A.: Phys. Rev. Lett. 76, 4656 (1996)ADSCrossRefGoogle Scholar
  20. 20.
    Ekert, A.K.: Phys. Rev. Lett. 67, 661 (1991)ADSMATHMathSciNetCrossRefGoogle Scholar
  21. 21.
    Moriya, T.: Phys. Rev. A 120, 91 (1960)ADSCrossRefGoogle Scholar
  22. 22.
    Maruyama, K., Iitaka, Y., Nori, F.: Phys. Rev. A 75, 012325 (2007)ADSCrossRefGoogle Scholar
  23. 23.
    Kargarian, M., Jafari, R., Langari, A.: Phys. Rev. A 79, 042319 (2009)ADSCrossRefGoogle Scholar
  24. 24.
    Cheng, W.W., Yin, Z.: Phys. Rev. A 81, 044304 (2010)ADSCrossRefGoogle Scholar
  25. 25.
    Liu, B.Q., Shao, B., Li, J.G., Zhou, J., Wu, L.A.: Phys. Rev. A 83, 052112 (2011)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.School of Physics and Information EngineeringShanxi Normal UniversityLinfenPeople’s Republic of China

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