Skip to main content
Log in

Criteria for non-k-separability of n-partite quantum states

  • Regular Article
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

We develop separability criteria to identify non-k-separability (k = 2,3, ... ,n) and genuine multipartite entanglement in different classes of mixed n-partite quantum states using elements of density matrices. With the help of these criteria, we detect non-k-separability in n-qudit GHZ and W states respectively added with white noise. We also discuss the experimental implementation of our criteria by means of local observables.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, Rev. Mod. Phys. 81, 865 (2009)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  2. O. Gühne, G. Tóth, Phys. Rep. 474, 1 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  3. R. Jozsa, N. Linden, Proc. R. Soc. A 459, 2011 (2003)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  4. A. Karlsson, M. Bourennane, Phys. Rev. A 58, 4394 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  5. M. Hillery, V. Bužek, A. Berthiaume, Phys. Rev. A 59, 1829 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  6. P. Agrawal, A. Pati, Phys. Rev. A 74, 062320 (2006)

    Article  ADS  Google Scholar 

  7. S.-B. Zheng, Phys. Rev. A 74, 054303 (2006)

    Article  ADS  Google Scholar 

  8. E. D’Hondt, P. Panangaden, Quantum Inf. Comput. 6, 173 (2006).

    MATH  MathSciNet  Google Scholar 

  9. D.M. Greenberger, M.A. Horne, A. Shimony, A. Zeilinger, Am. J. Phys. 58, 1131 (1990)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  10. J.D. Bancal, C. Branciard, N. Gisin, S. Pironio, Phys. Rev. Lett. 103, 090503 (2009)

    Article  ADS  Google Scholar 

  11. A. Cabello, Phys. Rev. A 65, 032108 (2002)

    Article  ADS  Google Scholar 

  12. A. Gabriel, B.C. Hiesmeyr, M. Huber, Quantum Inf. Comput. 10, 0829 (2010)

    Google Scholar 

  13. W. Dür, J.I. Cirac, R. Tarrach, Phys. Rev. Lett. 83, 3562 (1999)

    Article  ADS  Google Scholar 

  14. W. Dür, J.I. Cirac, Phys. Rev. A 61, 042314 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  15. W. Dür, J.I. Cirac, J. Phys. A 34, 6837 (2001)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  16. M. Seevinck, G. Svetlichny, Phys. Rev. Lett. 89, 060401 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  17. J. Uffink, Phys. Rev. Lett. 88, 230406 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  18. W. Laskowski, M. Zukowski, Phys. Rev. A 72, 062112 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  19. G. Tóth, O. Gühne, Phys. Rev. A 72, 022340 (2005)

    Article  ADS  Google Scholar 

  20. M. Seevinck, J. Uffink, Phys. Rev. A 78, 032101 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  21. M. Huber, F. Mintert, A. Gabriel, B.C. Hiesmeyr, Phys. Rev. Lett. 104, 210501 (2010)

    Article  ADS  Google Scholar 

  22. T. Gao, Y. Hong, Phys. Rev. A 82, 062113 (2010)

    Article  ADS  Google Scholar 

  23. O. Gühne, M. Seevinck, New J. Phys. 12, 053002 (2010)

    Article  Google Scholar 

  24. T. Gao, Y. Hong, Eur. Phys. J. D 61, 765 (2011)

    Article  ADS  Google Scholar 

  25. T. Gao, Y. Hong, Y. Lu, F. Yan, Europhys. Lett. 104, 20007 (2013)

    Article  ADS  Google Scholar 

  26. O. Gühne, C.-Y. Lu, W.-B. Gao, J.-W. Pan, Phys. Rev. A 76, 030305(R) (2007)

    Article  Google Scholar 

  27. Y. Lu, G.L. Long, T. Gao, Int. J. Theor. Phys. 52, 699 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  28. J.S. Kim, B.C. Sanders, J. Phys. A 41, 495301 (2008)

    Article  MathSciNet  Google Scholar 

  29. M. Huber, M.P. Llobet, J.I. de Vicente, Phys. Rev. A 88, 042328 (2013)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Senthilvelan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ananth, N., Chandrasekar, V.K. & Senthilvelan, M. Criteria for non-k-separability of n-partite quantum states. Eur. Phys. J. D 69, 56 (2015). https://doi.org/10.1140/epjd/e2015-50538-5

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/e2015-50538-5

Keywords

Navigation