Advertisement

Applied Physics B

, Volume 98, Issue 4, pp 617–622 | Cite as

Separability criteria and entanglement witnesses for symmetric quantum states

  • G. Tóth
  • O. Gühne
Article
First Online:

Abstract

We study the separability of symmetric bipartite quantum states and show that a single correlation measurement is sufficient to detect the entanglement of any bipartite symmetric state with a non-positive partial transpose. We also discuss entanglement conditions and entanglement witnesses for states with a positive partial transpose.

Keywords

Quantum State Density Matrix Entangle State Hermitian Operator Symmetric State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. Horodecki P. Horodecki, M. Horodecki, K. Horodecki, Rev. Mod. Phys. 81, 865 (2009) MathSciNetADSzbMATHCrossRefGoogle Scholar
  2. 2.
    O. Gühne, G. Tóth, Phys. Rep. 474, 1 (2009) MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    A. Peres, Phys. Rev. Lett. 77, 1413 (1996) MathSciNetADSzbMATHCrossRefGoogle Scholar
  4. 4.
    M. Horodecki, P. Horodecki, R. Horodecki, Phys. Lett. A 223, 1 (1996) MathSciNetADSzbMATHCrossRefGoogle Scholar
  5. 5.
    M. Horodecki, P. Horodecki, R. Horodecki, Phys. Rev. Lett. 80, 5239 (1998) MathSciNetADSzbMATHCrossRefGoogle Scholar
  6. 6.
    P. Horodecki, Phys. Lett. A 232, 333 (1997). For a review see P. Horodecki, in Lectures on Quantum Information, ed. by D. Bruß, G. Leuchs (Wiley-VCH, Berlin, 2006) MathSciNetADSzbMATHCrossRefGoogle Scholar
  7. 7.
    O. Rudolph, Quantum Inf. Proc. 4, 219 (2005) MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    K. Chen, L.-A. Wu, Quantum Inf. Comput. 3, 193 (2003) MathSciNetzbMATHGoogle Scholar
  9. 9.
    O. Gühne, P. Hyllus, O. Gittsovich, J. Eisert, Phys. Rev. Lett. 99, 130504 (2007) MathSciNetCrossRefGoogle Scholar
  10. 10.
    O. Gittsovich, O. Gühne, P. Hyllus, J. Eisert, Phys. Rev. A 78, 052319 (2008) ADSCrossRefGoogle Scholar
  11. 11.
    A.R. Usha Devi, M.S. Uma, R. Praphu, A.K. Rajagopal, Phys. Lett. A 364, 203 (2007) MathSciNetADSzbMATHCrossRefGoogle Scholar
  12. 12.
    A.R. Usha Devi, R. Prabhu, A.K. Rajagopal, Phys. Rev. Lett. 98, 060501 (2007) CrossRefGoogle Scholar
  13. 13.
    G. Tóth, O. Gühne, Phys. Rev. Lett. 102, 170503 (2009) MathSciNetADSCrossRefGoogle Scholar
  14. 14.
    E. Shchukin, W. Vogel, Phys. Rev. Lett. 95, 230502 (2005) ADSCrossRefGoogle Scholar
  15. 15.
    T. Moroder, M. Keyl, N. Lütkenhaus, J. Phys. A: Math. Theor. 41, 275302 (2008) ADSCrossRefGoogle Scholar
  16. 16.
    S. Yu, N.-L. Liu, Phys. Rev. Lett. 95, 150504 (2005) MathSciNetADSCrossRefGoogle Scholar
  17. 17.
    A. Sanpera, R. Tarrach, G. Vidal, Phys. Rev. A 58, 826 (1998) MathSciNetADSCrossRefGoogle Scholar
  18. 18.
    J. Korbicz, J.I. Cirac, J. Wehr, M. Lewenstein, Phys. Rev. Lett. 94, 153601 (2005) ADSCrossRefGoogle Scholar
  19. 19.
    J. Sperling, W. Vogel, Phys. Rev. A 79, 042337 (2009) MathSciNetADSCrossRefGoogle Scholar
  20. 20.
    J.A. Smolin, Phys. Rev. A 63, 032306 (2001) MathSciNetADSCrossRefGoogle Scholar
  21. 21.
    R. Augusiak, P. Horodecki, Phys. Rev. A 73, 012318 (2006) MathSciNetADSCrossRefGoogle Scholar
  22. 22.
    B.M. Terhal, Phys. Lett. A 271, 319 (2000) MathSciNetADSzbMATHCrossRefGoogle Scholar
  23. 23.
    D. Bruß, J.I. Cirac, P. Horodecki, F. Hulpke, B. Kraus, M. Lewenstein, A. Sanpera, J. Mod. Opt. 49, 1399 (2002) ADSzbMATHCrossRefGoogle Scholar
  24. 24.
    M. Lewenstein, B. Kraus, J.I. Cirac, P. Horodecki, Phys. Rev. A 62, 052310 (2000) ADSCrossRefGoogle Scholar
  25. 25.
    A. Sanpera, D. Bruß, M. Lewenstein, Phys. Rev. A 63, 050301 (2001) ADSCrossRefGoogle Scholar
  26. 26.
    B. Kraus, M. Lewenstein, J.I. Cirac, Phys. Rev. A 65, 042327 (2002) ADSCrossRefGoogle Scholar
  27. 27.
    P. Hyllus, C. Moura Alves, D. Bruß, C. Macchiavello, Phys. Rev. A 70, 032316 (2004) ADSCrossRefGoogle Scholar
  28. 28.
    K. Eckert, J. Schliemann, D. Bruß, M. Lewenstein, Ann. Phys. 299, 88 (2002) ADSzbMATHCrossRefGoogle Scholar
  29. 29.
    R. Hübener, M. Kleinmann, T.-C. Wei, C. González-Guillén, O. Gühne, Phys. Rev. A 80, 032324 (2009) MathSciNetADSCrossRefGoogle Scholar
  30. 30.
    A.C. Doherty, P.A. Parrilo, F.M. Spedalieri, Phys. Rev. Lett. 88, 187904 (2002) ADSCrossRefGoogle Scholar
  31. 31.
    F.G.S.L. Brandão, R.O. Vianna, Phys. Rev. Lett. 93, 220503 (2004) ADSCrossRefGoogle Scholar
  32. 32.
    J. Eisert, P. Hyllus, O. Gühne, M. Curty, Phys. Rev. A 70, 062317 (2004) ADSCrossRefGoogle Scholar
  33. 33.
    P. Hyllus, J. Eisert, New J. Phys. 8, 51 (2006) ADSCrossRefGoogle Scholar
  34. 34.
    M.A. Jafarizadeh, G. Najarbashi, H. Habibian, Phys. Rev. A 75, 052326 (2007) ADSCrossRefGoogle Scholar
  35. 35.
    M. Navascues, M. Owari, M.B. Plenio, Phys. Rev. Lett. 103, 160404 (2009) ADSCrossRefGoogle Scholar
  36. 36.
    L. Vandenberghe, S. Boyd, SIAM Rev. 38, 49 (1996) MathSciNetzbMATHCrossRefGoogle Scholar
  37. 37.
    J.B. Lasserre, SIAM J. Optim. 11, 796 (2000) MathSciNetCrossRefGoogle Scholar
  38. 38.
    J. Sturm, SeDuMi, a MATLAB toolbox for optimization over symmetric cones, URL http://sedumi.mcmaster.ca
  39. 39.
    J. Löfberg, Yalmip: A toolbox for modeling and optimization in MATLAB, URL http://control.ee.ethz.ch/~joloef/yalmip.php
  40. 40.

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Theoretical PhysicsThe University of the Basque CountryBilbaoSpain
  2. 2.IKERBASQUE, Basque Foundation for ScienceBilbaoSpain
  3. 3.Research Institute for Solid State Physics and OpticsHungarian Academy of SciencesBudapestHungary
  4. 4.Institut für Quantenoptik und QuanteninformationÖsterreichische Akademie der WissenschaftenInnsbruckAustria
  5. 5.Institut für Theoretische PhysikUniversität InnsbruckInnsbruckAustria

Personalised recommendations

Cite article

Buy options