SpringerLink
Log in

Entanglement, Quantum Discord, and Non-locality in Bell-Diagonal States

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

Experimental approach to characterize the non-locality, entanglement, and quantum correlation of a multiparity quantum system is one of the important subjects in quantum information theory. Here, by investigating the violations of Bell inequality (BI), we analyze the relations among the non-locality, concurrence C, and quantum discord Q typically for a family of Bell-diagonal states. It is shown that, for the optimal measurement basis the BI is always violated, if the quantum discord is larger than 0.5031 and the concurrence is larger than 0.5605. Certainly, the BI is maximally violated for the maximal entanglement and quantum discord, i.e., C=Q=1. Our generic results are demonstrated with a thermal XY model of the two-qubit system with controllable interbit couplings.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Einstein, A., Podolsky, B., Rosen, N.: Phys. Rev. 47, 777 (1935)

    Article  ADS  MATH  Google Scholar 

  2. Ekert, A.K.: Phys. Rev. Lett. 67, 661 (1991)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. Jennewein, T., Simon, C., Weihs, G., Weinfurter, H., Zeilinger, A.: Phys. Rev. Lett. 84, 4729 (2000)

    Article  ADS  Google Scholar 

  4. Horodecki, M., Piani, M.: J. Phys. A, Math. Theor. 45, 105306 (2012)

    Article  MathSciNet  ADS  Google Scholar 

  5. Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Phys. Rev. Lett. 70, 1895 (1993)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Hotta, M.: J. Phys. A, Math. Theor. 43, 105305 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  7. Choudhury, S., Muralidharan, S., Panigrahi, P.K.: J. Phys. A, Math. Theor. 42, 115303 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  8. Schumacher, B.: Phys. Rev. A 54, 2614 (1996)

    Article  ADS  Google Scholar 

  9. Hu, Z.D., Zhang, Y.Q., Xu, J.B.: J. Phys. A, Math. Theor. 42, 425303 (2011)

    Article  MathSciNet  Google Scholar 

  10. Bell, J.S.: Physics (N.Y.) 1, 195 (1964)

    Google Scholar 

  11. Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Phys. Rev. Lett. 23, 880 (1969)

    Article  ADS  Google Scholar 

  12. Fattal, D., Inoue, K., Vučković, J., Santori, C., Solomon, G.S., Yamamoto, Y.: Phys. Rev. Lett. 92, 037903 (2004)

    Article  ADS  Google Scholar 

  13. Simon, C., Irvine, W.T.M.: Phys. Rev. Lett. 91, 110405 (2003)

    Article  ADS  Google Scholar 

  14. Wei, L.F., Liu, Y.X., Nori, F.: Phys. Rev. B 72, 104516 (2005)

    Article  ADS  Google Scholar 

  15. Wei, L.F., Liu, Y.X., Storcz, M.J., Nori, F.: Phys. Rev. A 73, 052307 (2006)

    Article  ADS  Google Scholar 

  16. Braunstein, S.L., Mann, A., Revzen, M.: Phys. Rev. Lett. 68, 3259 (1992)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. Horodecki, R., Horodecki, P., Horodecki, M.: Phys. Lett. A 200, 340–344 (1995)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. Verstraete, F., Wolf, M.M.: Phys. Rev. Lett. 89, 170401 (2002)

    Article  ADS  Google Scholar 

  19. Wootters, W.K.: Phys. Rev. Lett. 80, 2245 (1998)

    Article  ADS  Google Scholar 

  20. Ollivier, H., Zurek, W.H.: Phys. Rev. Lett. 88, 017901 (2001)

    Article  ADS  Google Scholar 

  21. Vedral, V.: Phys. Rev. Lett. 90, 050401 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  22. Rajagopal, A.K., Rendell, R.W.: Phys. Rev. A 66, 022104 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  23. Hofmann, H.F.: J. Phys. A, Math. Theor. 42, 275304 (2009)

    Article  ADS  Google Scholar 

  24. Batle, J., Plastino, A., Plastino, A.R., Casas, M.: J. Phys. A, Math. Theor. 44, 505304 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  25. Baumgartner, B., Hiesmayr, B.C., Narnhofer, H.: Phys. Rev. A 74, 032327 (2006)

    Article  ADS  Google Scholar 

  26. Bertlmann, R.A., Krammer, P.: Phys. Rev. A 78, 014303 (2008)

    Article  ADS  Google Scholar 

  27. Baumgartner, B., Hiesmayr, B., Narnhofer, H.: Phys. Lett. A 372, 2190 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  28. Bohm, D.: In: Quantum Theory, p. 611. Prentice-Hall, Englewood Cliffs (1951). Ch. 22

    Google Scholar 

  29. Kent, A., Linden, N., Massar, S.: Phys. Rev. Lett. 83, 2656 (1999)

    Article  ADS  Google Scholar 

  30. Verstraete, F., Verschelde, H.: Phys. Rev. Lett. 90, 097901 (2003)

    Article  ADS  Google Scholar 

  31. Wang, Z.W., Zhou, X.F., Huang, Y.F., Zhang, Y.S., Ren, X.F., Guo, G.C.: Phys. Rev. Lett. 96, 220505 (2006)

    Article  ADS  Google Scholar 

  32. Huang, J.H., Zhu, S.Y.: J. Phys. A, Math. Theor. 41, 125301 (2008)

    Article  MathSciNet  Google Scholar 

  33. Koashi, M., Imoto, N.: Phys. Rev. Lett. 77, 2137 (1996)

    Article  ADS  Google Scholar 

  34. Marais, A., Konrad, T., Petruccione, F.: J. Phys. A, Math. Theor. 30, 305302 (2010)

    Article  MathSciNet  Google Scholar 

  35. Bennett, C.H., DiVincenzo, D.P., Smolin, J.A., Wootters, W.K.: Phys. Rev. A 54, 3824 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  36. Batle, J., Casas, M.: J. Phys. A, Math. Theor. 44, 445304 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  37. Luo, S.: Phys. Rev. A 77, 042303 (2008)

    Article  ADS  Google Scholar 

  38. Cirel’son, B.S.: Lett. Math. Phys. 4, 93 (1980)

    Article  MathSciNet  ADS  Google Scholar 

  39. Lieb, E., Schultz, T., Mattis, D.: Ann. Phys. (N.Y.) 16, 407 (1961)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  40. Éboli, O., Jackiw, R., Pi, S.Y.: Phys. Rev. D 37, 3557 (1988)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the National Science Foundation grant Nos. 90921010, 11174373, and the National Fundamental Research Program of China through Grant No. 2010CB923104.

Author information

Authors and Affiliations

  1. Quantum Optoelectronics Laboratory, School of Physics and Technology, Southwest Jiaotong University, Chengdu, 610031, China

    Zhi-Li Zhou, Hao Yuan & Lian-Fu Wei

  2. State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics Science and Engineering, Sun Yet-sen University, Guangzhou, 510275, China

    Lian-Fu Wei

Authors
  1. Zhi-Li Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hao Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lian-Fu Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lian-Fu Wei.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhou, ZL., Yuan, H. & Wei, LF. Entanglement, Quantum Discord, and Non-locality in Bell-Diagonal States. Int J Theor Phys 52, 420–428 (2013). https://doi.org/10.1007/s10773-012-1348-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-012-1348-7

Keywords

Search

Navigation