Advertisement

Detecting two qubit both-way positive discord states

  • Kaushiki Mukherjee
  • Sumana Karmakar
  • Biswajit Paul
  • Debasis SarkarEmail author
Regular Article
  • 20 Downloads

Abstract

Quantum discord plays a pragmatic role in analyzing nonclassical feature of quantum correlations beyond entanglement. It is used in several information processing protocols which lacks sufficient amount of entanglement to be used as a resource. We have provided with an analytical method of detecting quantum discord of an arbitrary two qubit state. We have formulated a set of necessary and sufficient conditions for any two qubit state to be a both-way non-zero quantum discord state. As quantum discord is asymmetric in nature, we have framed the set of if and only if conditions for a two qubit state to be classical-quantum as well for it to be quantum-classical. Interestingly, not only correlation tensor but also local Bloch vector (corresponding to the classical party) plays a role for detecting the state to be a positive discord state.

Graphical abstract

Keywords

Quantum Information 

References

  1. 1.
    R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, Rev. Mod. Phys. 81, 865 (2009)ADSCrossRefGoogle Scholar
  2. 2.
    A. Datta, A. Shaji, C.M. Caves, Phys. Rev. Lett. 100, 050502 (2008)ADSCrossRefGoogle Scholar
  3. 3.
    H. Ollivier, W.H. Zurek, Phys. Rev. Lett. 88, 017901 (2001)ADSCrossRefGoogle Scholar
  4. 4.
    M.D. Lang, C.M. Caves, A. Shaji, Int. J. Quantum. Inform. 9, 1553 (2011)CrossRefGoogle Scholar
  5. 5.
    A. Datta, Phys. Rev. A 80, 052304 (2009)ADSCrossRefGoogle Scholar
  6. 6.
    B. Bylicka, D. Chruscinski, Phys. Rev. A 81, 062102 (2010)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    B. Dakic, V. Vedral, C. Brukner, Phys. Rev. Lett. 105, 190502 (2010)ADSCrossRefGoogle Scholar
  8. 8.
    J. Maziero, R.M. Serra, Int. J. Quantum. Inform. 10, 1250028 (2012)CrossRefGoogle Scholar
  9. 9.
    A. Ferraro, L. Aolita, D. Cavalcanti, F.M. Cucchietti, A. Acin, Phys. Rev. A 81, 052318 (2010)ADSCrossRefGoogle Scholar
  10. 10.
    D. Girolami, G. Adesso, Phys. Rev. A 83, 052108 (2011)ADSCrossRefGoogle Scholar
  11. 11.
    R. Laflamme, D.G. Cory, C. Negrevergne, L. Viola, Quantum Inf. Comput. 2, 166 (2002)MathSciNetGoogle Scholar
  12. 12.
    J. Oppenheim, M. Horodecki, P. Horodecki, R. Horodecki, Phys. Rev. Lett. 89, 180402 (2002)ADSCrossRefGoogle Scholar
  13. 13.
    Z. Merali, Nature (London) 474, 24 (2011)ADSCrossRefGoogle Scholar
  14. 14.
    K. Modi, A. Brodutch, H. Cable, T. Paterek, V. Vedral, Rev. Mod. Phys. 84, 1655 (2012)ADSCrossRefGoogle Scholar
  15. 15.
    A. Brodutch, D.R. Terno, Phys. Rev. A 83, 010301 (2011)ADSCrossRefGoogle Scholar
  16. 16.
    V. Giovannetti, S. Lloyd, L. Maccone, Phys. Rev. Lett. 96, 010401 (2006)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    K. Modi, H. Cable, M. Williamson, V. Vedral, Phys. Rev. X 1, 021022 (2011)Google Scholar
  18. 18.
    S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, England, 2000)Google Scholar
  19. 19.
    L. Amico, R. Fazio, A. Osterloh, V. Vedral, Rev. Mod. Phys. 80, 517 (2008)ADSCrossRefGoogle Scholar
  20. 20.
    M. Piani, P. Horodecki, R. Horodecki, Phys. Rev. Lett. 100, 090502 (2008)ADSCrossRefGoogle Scholar
  21. 21.
    M. Horodecki, J. Oppenheim, A. Winter, Nature 436, 673 (2005)ADSCrossRefGoogle Scholar
  22. 22.
    M. Horodecki, J. Oppenheim, A. Winter, Comm. Math. Phys. 269, 107 (2007)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    M.A. Nielsen, I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000)Google Scholar
  24. 24.
    W.H. Zurek, Ann. Phys. (Leipzig) 9, 855 (2000)ADSCrossRefGoogle Scholar
  25. 25.
    M. Zwolak, H.T. Quan, W.H. Zurek, Phys. Rev. A 81, 062110 (2010)ADSCrossRefGoogle Scholar
  26. 26.
    K. Maruyama, F. Nori, V. Vedral, Rev. Mod. Phys. 81, 1 (2009)ADSCrossRefGoogle Scholar
  27. 27.
    R. Srikanth, S. Banerjee, C.M. Chandrashekar, Phys. Rev. A 81, 062123 (2010)ADSCrossRefGoogle Scholar
  28. 28.
    G.L. Giorgi, F. Galve, G. Manzano, P. Colet, R. Zambrini, Phys. Rev. A 85, 052101 (2012)ADSCrossRefGoogle Scholar
  29. 29.
    T. Yu, J.H. Eberly, Quantum Inform. Comput. 7, 459 (2007)Google Scholar
  30. 30.
    A.R.P. Rau, J. Phys. A: Math. Theor. 42, 412002 (2009)CrossRefGoogle Scholar
  31. 31.
    R.F. Werner, Phys. Rev. A 40, 4277 (1989)ADSCrossRefGoogle Scholar
  32. 32.
    D. Cavalcanti, L. Aolita, S. Boixo, K. Modi, M. Piani, A. Winter, Phys. Rev. A 83, 032324 (2011)ADSCrossRefGoogle Scholar
  33. 33.
    H. Barnum, C. Caves, C. Fuchs, R. Jozsa, B. Schumacher, Phys. Rev. Lett. 76, 2818 (1996)ADSCrossRefGoogle Scholar
  34. 34.
    W.K. Wootters, W.H. Zurek, Nature (London) 299, 802 (1982)ADSCrossRefGoogle Scholar
  35. 35.
    S. Luo, Lett. Math. Phys. 92, 143 (2010)ADSMathSciNetCrossRefGoogle Scholar
  36. 36.
    S. Luo, N. Li, X. Cao, Phys. Rev. A 79, 054305 (2009)ADSCrossRefGoogle Scholar
  37. 37.
    S. Luo, W. Sun, Phys. Rev. A 82, 012338 (2010)ADSCrossRefGoogle Scholar
  38. 38.
    G. Adesso, A. Datta, Phys. Rev. Lett. 105, 030501 (2010)ADSCrossRefGoogle Scholar
  39. 39.
    G. Adesso, D. Girolami, Int. J. Quantum. Inform. 9, 1773 (2011)CrossRefGoogle Scholar

Copyright information

© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Kaushiki Mukherjee
    • 1
  • Sumana Karmakar
    • 2
  • Biswajit Paul
    • 3
  • Debasis Sarkar
    • 4
    Email author
  1. 1.Department of MathematicsGovernment Girls’ General Degree CollegeEkbalporeIndia
  2. 2.Department of MathematicsHeritage Institute of TechnologyAnandapurIndia
  3. 3.Department of MathematicsSouth Malda CollegeMaldaIndia
  4. 4.Department of Applied MathematicsUniversity of CalcuttaKolkataIndia

Personalised recommendations