Advertisement

Entanglement witnesses and characterizing entanglement properties of some PPT states

  • M. A. JafarizadehEmail author
  • N. Behzadi
  • Y. Akbari
Quantum Information

Abstract

On the basis of linear programming, new sets of entanglement witnesses (EWs) for 3⊗3 and 4⊗4 systems are constructed. In both cases, the constructed EWs correspond to the hyper-planes contacting, without intersecting, the related feasible regions at line segments and restricted planes respectively. Due to the special property of the contacting area between the hyper-planes and the feasible regions, the corresponding hyper-planes can be turned around the contacting area throughout a bounded interval and hence create an infinite number of EWs. As these EWs are able to detect entanglement of some PPT states, they are non-decomposable (nd-EWs).

PACS

03.67.Mn Entanglement measures, witnesses, and other characterizations 03.65.Ud Entanglement and quantum nonlocality 

References

  1. M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000) Google Scholar
  2. The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation and Quantum Computation, edited by D. Bouwmeester, A. Ekert, A. Zeilinger (Springer, New York, 2000) Google Scholar
  3. J. Preskill, The Theory of Quantum Information and Quantum Computation (California Institute of Technology, Pasadena, CA, 2000), http://www.theory.caltech.edu/poeole/preskill/ph229/ Google Scholar
  4. A. Peres, Phys. Rev. Lett. 77, 1413 (1996) Google Scholar
  5. P. Horodecki, Phys. Lett. A 232, 333 (1997) Google Scholar
  6. M. Horodecki, P. Horodecki, R. Horodecki, Phys. Rev. Lett. 80, 5239, (1998) Google Scholar
  7. M. Horodecki, P. Horodecki, R. Horodecki, Phys. Lett. A 223, 1 (1996) Google Scholar
  8. B.M. Terhal, Phys. Lett. A 271, 319 (2000); B.M. Terhal, Linear Algebr. Appl. 323, 61 (2000) Google Scholar
  9. S. L. Woronowicz, Rep. Math. Phys. 10, 165 (1976) Google Scholar
  10. S. Boyd, L. Vandenberghe, Convex Optimization (Cambridge University Press, 2004) Google Scholar
  11. E.K.P. Chong, S.H. Zak, An Introduction to Optimization (John Wiley, NY, 2001) Google Scholar
  12. M.A. Jafarizadeh, M. Rezaee, S.K.A. Seyed Yagoobi, Phys. Rev. A 72, 062106 (2005) Google Scholar
  13. M.A. Jafarizadeh, R. Sufiani, Phys. Rev. A 77, 012105 (2008) Google Scholar
  14. M.A. Jafarizadeh, G. Najarbashi, Y. Akbari, H. Habibian, Eur. Phys. J. D 47, 233 (2008) Google Scholar
  15. M.A. Jafarizadeh, Y. Akbari, N. Behzadi, Eur. Phys. J. D 47, 283 (2008) Google Scholar
  16. M. Horodecki, P. Horodecki, R. Horodecki, Phys. Rev. Lett. 82, 1056 (1999) Google Scholar
  17. A.C. Doherty, P.A. Parrilo, F.M. Spedalieri, Phys. Rev. Lett. 88, 187904 (2002) Google Scholar
  18. O. Gühne, P. Hyllus, Int. J. Theor. Phys., 42, No. 5, 2003 Google Scholar
  19. G. Tóth, O. Gühne, Phys. Rev. Lett. 94, 060501 (2005) Google Scholar
  20. W. Pfeifer, The Lie Algebras su(N) An Introduction (Birkhäuser Verlag, 2003) Google Scholar
  21. H. P. Breuer, Phys. Rev. A 71, 062330 (2005) Google Scholar
  22. H. P. Breuer, J. Phys. A: Math. Gen. 38, 90199037 (2005) Google Scholar
  23. H. P. Breuer, Phys. Rev. Lett. 97, 080501 (2006) Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  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.Department of PhysicsAzarbaijan University of Tarbiat MoallemTabrizIran

Personalised recommendations