Advertisement

International Journal of Theoretical Physics

, Volume 55, Issue 3, pp 1543–1557 | Cite as

Quantum Discord of 2 n -Dimensional Bell-Diagonal States

  • M. A. Jafarizadeh
  • N. Karimi
  • D. Amidi
  • H. Zahir Olyaei
Article

Abstract

In this study, using the concept of relative entropy as a distance measure of correlations we investigate the important issue of evaluating quantum correlations such as entanglement, dissonance and classical correlations for 2 n -dimensional Bell-diagonal states. We provide an analytical technique, which describes how we find the closest classical states(CCS) and the closest separable states(CSS) for these states. Then analytical results are obtained for quantum discord of 2 n -dimensional Bell-diagonal states. As illustration, some special cases are examined. Finally, we investigate the additivity relation between the different correlations for the separable generalized Bloch sphere states.

Keywords

Quantum discord Distance measure of correlations Dirac γ matrices Bipartite quantum system 

References

  1. 1.
    Bennett, C.H., et al.: Phys. Rev. Lett. 70, 1895 (1993)ADSMATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Horodecki, R., Horodecki, P., Horodecki, M.: Phys. Lett. A 200, 340 (1995)ADSMATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Bennett, C.H., Wiesner, S.J.: Phys. Rev. Lett. 69, 2881 (1992)ADSMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Pati, A.K.: Rev. Phys. A 014320, 63 (2001)Google Scholar
  5. 5.
    Gisin, N., et al.: Rev. Mod. Phys. 74, 145 (2002)ADSCrossRefGoogle Scholar
  6. 6.
    Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Rev. Mod. Phys. 81, 865 (2009)ADSMATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    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
  8. 8.
    Niset, J., Cerf, N.J.: Phys. Rev. A 052103, 74 (2006)Google Scholar
  9. 9.
    Datta, A., Flammia, A.T., Caves, C.M.: Phys. Rev. A 72, 042316 (2005)ADSCrossRefGoogle Scholar
  10. 10.
    Datta, A., Vidal, G.: Phys. Rev. A 75, 042310 (2007)ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    Datta, A.: Phys. Rev. A 80, 052304 (2009)ADSCrossRefGoogle Scholar
  12. 12.
    Datta, A., Shaji, A., Caves, C.M.: Phys. Rev. Lett. 050502, 100 (2008)Google Scholar
  13. 13.
    Lanyon, B.P., Barbieri, M., Almeida, M.P., White, A.G.: Phys. Rev. Lett. 200501, 101 (2008)Google Scholar
  14. 14.
    Ollivier, H., Zurek, W.H.: Phys. Rev. Lett. 017901, 88 (2001)Google Scholar
  15. 15.
    Henderson, L., Vedral, V.: J. Phys. A 34, 6899 (2001)ADSMATHMathSciNetCrossRefGoogle Scholar
  16. 16.
    Bylicka, B., ChruLsciLnski, D.: Phys. Rev. A 062102, 81 (2010)Google Scholar
  17. 17.
    Werlang, T., Souza, S., Fanchini, F.F., Villas Boas, C.J.: Phys. Rev. A 024103, 80 (2009)Google Scholar
  18. 18.
    Sarandy, M.S.: Rev. Phys. A 022108, 80 (2009)Google Scholar
  19. 19.
    Ferraro, A., Aolita, L., Cavalcanti, D., Cucchietti, F. M., AcL.n, A.: Phys. Rev. A 052318, 81 (2010)Google Scholar
  20. 20.
    Fanchini, F.F., Werlang, T., Brasil, C.A., Arruda, L.G.E., Caldeira, A.O.: Phys. Rev. A 052107, 81 (2010)Google Scholar
  21. 21.
    DakL.c, B., Vedral, V., Brukner, C.: Phys. Rev. Lett. 190502, 105 (2010)Google Scholar
  22. 22.
    Modi, K., Paterek, T., Son, W., Vedral, V., Williamson, M.: Phys. Rev. Lett. 080501, 104 (2010)MathSciNetGoogle Scholar
  23. 23.
    Li, N., Luo, S.: Phys. Rev. A 76, 032327 (2007)ADSCrossRefGoogle Scholar
  24. 24.
    Luo, S.: Phys. Rev. A 022301, 77 (2008)Google Scholar
  25. 25.
    Luo, S.: Rev. Phys. A 042303, 77 (2008)Google Scholar
  26. 26.
    Lang, M.D., Caves, C.M.: Phys. Rev. Lett. 150501, 105 (2010)Google Scholar
  27. 27.
    Ali, M., Rau, A.R.P., Alber, G.: Phys. Rev. A 81, 042105 (2010)ADSCrossRefGoogle Scholar
  28. 28.
    Ali, M., Rau, A.R.P., Alber, G.: Phys. Rev. A 069902, 82 (2010)Google Scholar
  29. 29.
    Mazzola, L., Piilo, J., Maniscalco, S.: Phys. Rev. Lett. 200401, 104 (2010)MathSciNetGoogle Scholar
  30. 30.
    Maziero, J., CLeleri, L.C., Serra, R.M., Vedral, V.: Phys. Rev. A 044102, 80 (2009)Google Scholar
  31. 31.
    Ma, Z., Chen, Z., Fanchini, F.F., Fei, S.: Sci. Rep. 5, 10262 (2015)ADSCrossRefGoogle Scholar
  32. 32.
    Modi, K.: Open. Syst. Inf. Dyn. 1440006, 21 (2014)MathSciNetGoogle Scholar
  33. 33.
    Zhang, J.S., Chen, A.X.: Quant. Phys. Lett. 1(2), 69–77 (2012)ADSGoogle Scholar
  34. 34.
    Open problems in Quntum information theory at http://www.imaph.tu-bs.de/qi/problems/8.html
  35. 35.
    Kim, H., Hwang, M.-R., Jung, E., Park, D.K.: Phys. Rev. A 052325, 81 (2010)Google Scholar
  36. 36.
    Vedral, V., Plenio, M.B., Rippin, M.A., Knight, P.L.: Phys. Rev. Lett. 78, 2275 (1997)ADSMATHMathSciNetCrossRefGoogle Scholar
  37. 37.
    Vedral, V., Plenio, M.B.: Phys. Rev. A 57, 1619 (1998)ADSCrossRefGoogle Scholar
  38. 38.
    Verstraete, F., Audenaert, K., De Moor, B.: Phys. Rev. A 012316, 64 (2001)Google Scholar
  39. 39.
    Verstraete, F., Audenaert, K.M.R., Dehaene, J., Moor, B.D.: J. Phys. A 34, 10327 (2001)ADSMATHMathSciNetCrossRefGoogle Scholar
  40. 40.
    Verstraete, F., Dehaene, J., De Moor, B.: J. Mod. Opt. 49, 1277 (2002)ADSMATHMathSciNetCrossRefGoogle Scholar
  41. 41.
    Audenaert, K.M.R., De Moor, B., Vollbrecht, K.G.H., Werner, R.F.: Phys. Rev. A 032310, 66 (2002)Google Scholar
  42. 42.
    Miranowicz, A., Grudka, A.: J. Opt. B: Quantum Semiclassical Opt. 6, 542 (2004)ADSCrossRefGoogle Scholar
  43. 43.
    Wei, T.C., Ericsson, M., Goldbart, P., Munro, W.J.: Quantum Inf. Comput. 4, 252 (2004)MATHMathSciNetGoogle Scholar
  44. 44.
    Parashar, P., Rana, S.: Phys. Rev. A 83(032301), 3 (2011)Google Scholar
  45. 45.
    Eisert, J.: e-print arXiv:quant-ph/0504166v1
  46. 46.
    Miranowicz, A., Ishizaka, S.: Phys. Rev. A 032310, 78 (2008)MathSciNetGoogle Scholar
  47. 47.
    Friedland, S., Gour, G.: J. Math. Phys. 052201, 52 (2011)MathSciNetGoogle Scholar
  48. 48.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)MATHGoogle Scholar
  49. 49.
    Jafarizadeh, M.A., Karimi, N., Zahir, H.: Eur. Phys. J. D 68, 136 (2014)ADSCrossRefGoogle Scholar
  50. 50.
    Jafarizadeh, M.A., Sufiani, R.: Phys. Rev. A 012105, 77 (2008)Google Scholar
  51. 51.
    Boyd, S., Vandenberghe, L.: Convex Optimization (Cambridge University Press, 2004)Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • M. A. Jafarizadeh
    • 1
    • 2
    • 3
  • N. Karimi
    • 2
    • 4
  • D. Amidi
    • 1
    • 2
  • H. Zahir Olyaei
    • 1
    • 2
  1. 1.Department of Theoretical Physics and AstrophysicsTabriz UniversityTabrizIran
  2. 2.Institute for Studies in Theoretical Physics and MathematicsTehranIran
  3. 3.Research Institute for Fundamental SciencesTabrizIran
  4. 4.Farhangian UniversityTabrizIran

Personalised recommendations