Persistence of quantum correlations in a XY spin-chain environment

  • Josep BatleEmail author
  • Mymona Abutalib
  • Soliman Abdalla
  • Ahmed Farouk
Regular Article


Quantum correlations in a physical system are usually degraded whenever there is an interaction with the environment. Here we consider the action of a XY spin-chain interacting with a system of two qubits. Results are surprising for particular families of states since their evolution does not destroy the presence of either entanglement or nonlocality, that is, those correlations persist for any possible configuration of the environment. In addition, we unveil the form of those states which, although being mixed, their entanglement implies nonlocality and vice versa. This finding constitutes an extension of the well-known Gisin Theorem for pure states of two qubits. The ensuing form will enable us to find the evolved entanglement and nonlocality in an analytical fashion.


Mesoscopic and Nanoscale Systems 


  1. 1.
    Introduction to Quantum Computation and Information, edited by H.-K. Lo, S. Popescu, T. Spiller (World Scientific, River-Edge, 1998)Google Scholar
  2. 2.
    A. Galindo, M.A. Martín-Delgado, Rev. Mod. Phys. 74, 347 (2002)ADSCrossRefGoogle Scholar
  3. 3.
    M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000)Google Scholar
  4. 4.
    C.P. Williams, S.H. Clearwater, Explorations in Quantum Computing (Springer, New York, 1997)Google Scholar
  5. 5.
    Quantum Computing and Quantum Communications, edited by C.P. Williams (Springer, Berlin, 1998)Google Scholar
  6. 6.
    A. Ekert, Phys. Rev. Lett. 67, 661 (1991)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    C.H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, W.K. Wootters, Phys. Rev. Lett. 70, 1895 (1993)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    C.H. Bennett, S.J. Wiesner, Phys. Rev. Lett. 69, 2881 (1993)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    A. Ekert, R. Jozsa, Rev. Mod. Phys. 68, 773 (1996)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    G.P. Berman, G.D. Doolen, R. Mainieri, V.I. Tsifrinovich, Introduction to Quantum Computers (World Scientific, Singapore, 1998)Google Scholar
  11. 11.
    J. Batle, M. Casas, Phys. Rev. A 82, 062101 (2010)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    J. Batle, M. Casas, J. Phys. A 44, 445304 (2011)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    C. Brukner, M. Zukowski, A. Zeilinger, Phys. Rev. Lett. 89, 197901 (2002)ADSCrossRefGoogle Scholar
  14. 14.
    J. Barrett, L. Hardy, A. Kent, Phys. Rev. Lett. 95, 010503 (2005)ADSCrossRefGoogle Scholar
  15. 15.
    A. Acín, N. Gisin, Ll. Masanes, Phys. Rev. Lett. 97, 120405 (2006)ADSCrossRefGoogle Scholar
  16. 16.
    A. Acín et al., Phys. Rev. Lett. 98, 230501 (2007)ADSCrossRefGoogle Scholar
  17. 17.
    Zi-Gang Yuan, Ping Zhang, Shu-Shen Li, Phys. Rev. A 76, 042118 (2007)ADSCrossRefGoogle Scholar
  18. 18.
    N. Gisin, Phys. Lett. A 154, 201 (1991)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    P. Jordan, E. Wigner, Z. Phys. 47, 631 (1928)ADSCrossRefGoogle Scholar
  20. 20.
    J.F. Clauser, M.A. Horne, A. Shimony, R.A. Holt, Phys. Rev. Lett. 23, 880 (1969)ADSCrossRefGoogle Scholar
  21. 21.
    B.S. Tsirelson, Lett. Math. Phys. 4, 93 (1980)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    B.S. Tsirelson, J. Soviet Math. 36, 557 (1987)CrossRefGoogle Scholar
  23. 23.
    B. S. Tsirelson, Hadronic J. Suppl. 8, 329 (1993)MathSciNetGoogle Scholar
  24. 24.
    R.F. Werner, Phys. Rev. A 40, 4277 (1989)ADSCrossRefGoogle Scholar
  25. 25.
    C.H. Bennett, D.P. DiVicenzo, J. Smolin, W.K. Wootters, Phys. Rev. A 54, 3824 (1996)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    W.K. Wootters, Phys. Rev. Lett. 80, 2245 (1998)ADSCrossRefGoogle Scholar
  27. 27.
    F. Verstraete, M.M. Wolf, Phys. Rev. Lett 89, 170401 (2002)ADSCrossRefGoogle Scholar
  28. 28.
    W.J. Munro, D.F.V. James, A.G. White, P.G. Kwiat, Phys. Rev. A 64, 030302 (2001)ADSCrossRefGoogle Scholar
  29. 29.
    Tzu-Chieh Wei, K. Nemoto, P.M. Goldbart, P.G. Kwiat, W.J. Munro, F. Verstraete, Phys. Rev. A 67, 022110 (2003)ADSCrossRefGoogle Scholar
  30. 30.
    J. Batle, M. Casas, A. Plastino, A.R. Plastino, Phys. Rev. A 71, 024301 (2005)ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    N.A. Peters, J.B. Altepeter, D. Branning, E.R. Jeffrey, T.-C. Wei, P.G. Kwiat Phys. Rev. Lett. 92, 133601 (2004)ADSCrossRefGoogle Scholar
  32. 32.
    M. Barbieri, F. De Martini, G. Di Nepi, P. Mataloni, Phys. Rev. Lett. 92, 177901 (2004)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Josep Batle
    • 1
    Email author
  • Mymona Abutalib
    • 2
  • Soliman Abdalla
    • 3
  • Ahmed Farouk
    • 4
  1. 1.Departament de Física, Universitat de les Illes BalearsBalearic IslandsSpain
  2. 2.Department of PhysicsFaculty of Science, Al Faisaliah Campus, King Abdulaziz UniversityJeddahSaudi Arabia
  3. 3.Department of PhysicsFaculty of Science, King Abdulaziz University JeddahJeddahSaudi Arabia
  4. 4.Information Technology DepartmentMuscatOman

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