Skip to main content
SpringerLink
Log in

Entanglement witnesses and characterizing entanglement properties of some PPT states

  • Quantum Information
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

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).

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000)

  • The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation and Quantum Computation, edited by D. Bouwmeester, A. Ekert, A. Zeilinger (Springer, New York, 2000)

  • 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/

  • A. Peres, Phys. Rev. Lett. 77, 1413 (1996)

    Google Scholar 

  • P. Horodecki, Phys. Lett. A 232, 333 (1997)

    Google Scholar 

  • M. Horodecki, P. Horodecki, R. Horodecki, Phys. Rev. Lett. 80, 5239, (1998)

    Google Scholar 

  • M. Horodecki, P. Horodecki, R. Horodecki, Phys. Lett. A 223, 1 (1996)

    Google Scholar 

  • B.M. Terhal, Phys. Lett. A 271, 319 (2000); B.M. Terhal, Linear Algebr. Appl. 323, 61 (2000)

    Google Scholar 

  • S. L. Woronowicz, Rep. Math. Phys. 10, 165 (1976)

    Google Scholar 

  • S. Boyd, L. Vandenberghe, Convex Optimization (Cambridge University Press, 2004)

  • E.K.P. Chong, S.H. Zak, An Introduction to Optimization (John Wiley, NY, 2001)

  • M.A. Jafarizadeh, M. Rezaee, S.K.A. Seyed Yagoobi, Phys. Rev. A 72, 062106 (2005)

  • M.A. Jafarizadeh, R. Sufiani, Phys. Rev. A 77, 012105 (2008)

  • M.A. Jafarizadeh, G. Najarbashi, Y. Akbari, H. Habibian, Eur. Phys. J. D 47, 233 (2008)

    Google Scholar 

  • M.A. Jafarizadeh, Y. Akbari, N. Behzadi, Eur. Phys. J. D 47, 283 (2008)

  • M. Horodecki, P. Horodecki, R. Horodecki, Phys. Rev. Lett. 82, 1056 (1999)

    Google Scholar 

  • A.C. Doherty, P.A. Parrilo, F.M. Spedalieri, Phys. Rev. Lett. 88, 187904 (2002)

    Google Scholar 

  • O. Gühne, P. Hyllus, Int. J. Theor. Phys., 42, No. 5, 2003

  • G. Tóth, O. Gühne, Phys. Rev. Lett. 94, 060501 (2005)

    Google Scholar 

  • W. Pfeifer, The Lie Algebras su(N) An Introduction (Birkhäuser Verlag, 2003)

  • H. P. Breuer, Phys. Rev. A 71, 062330 (2005)

    Google Scholar 

  • H. P. Breuer, J. Phys. A: Math. Gen. 38, 90199037 (2005)

    Google Scholar 

  • H. P. Breuer, Phys. Rev. Lett. 97, 080501 (2006)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Theoretical Physics and Astrophysics, Tabriz University, Tabriz, 51664, Iran

    M. A. Jafarizadeh & N. Behzadi

  2. Institute for Studies in Theoretical Physics and Mathematics, Tehran, 19395-1795, Iran

    M. A. Jafarizadeh & N. Behzadi

  3. Research Institute for Fundamental Sciences, Tabriz, 51664, Iran

    M. A. Jafarizadeh

  4. Department of Physics, Azarbaijan University of Tarbiat Moallem, 53714-161, Tabriz, Iran

    Y. Akbari

Authors
  1. M. A. Jafarizadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. Behzadi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Y. Akbari
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. A. Jafarizadeh.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jafarizadeh, M., Behzadi, N. & Akbari, Y. Entanglement witnesses and characterizing entanglement properties of some PPT states. Eur. Phys. J. D 55, 197–203 (2009). https://doi.org/10.1140/epjd/e2009-00176-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjd/e2009-00176-7

PACS

Search

Navigation