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International Journal of Theoretical Physics

, Volume 54, Issue 8, pp 3018–3025 | Cite as

Separability Criteria and Lower Bound for Concurrence Based on Hermitian Maps

  • Hao Guo
  • Fei Qi
  • Qiang Lei
Article
  • 136 Downloads

Abstract

In this paper, a class of matrix maps be preserving Hermitian are constructed. Based on these maps, for pure quantum states on any finite dimensional bipartite systems, we present a necessary and sufficient condition for separability, moreover, a new lower bound of concurrence is obtained.

Keywords

Quantum states Entanglement Concurrence 

Notes

Acknowledgments

This project is supported by China Postdoctoral Science Foundation (2014M551655) and Natural Science Foundation of Jiangsu Province of China (BK20130325).

References

  1. 1.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)MATHGoogle Scholar
  2. 2.
    Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Rev. Mod. Phys 81, 865 (2009)MathSciNetADSCrossRefMATHGoogle Scholar
  3. 3.
    Wootters, W.K.: Phys. Rev. Lett 80, 2245 (1998)ADSCrossRefGoogle Scholar
  4. 4.
    Chen, K., Albeverio, S., Fei, S.M.: Phys. Rev. Lett 95, 040504 (2005)MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    Breuer, H.P.: J. Phys. A 39 (1), 2006 (1847)Google Scholar
  6. 6.
    de Vicente, J.I.: Phys. Rev. A 75 (05), 2320 (2007)MathSciNetADSCrossRefMATHGoogle Scholar
  7. 7.
    Zhang, C.J., Zhang, Y.S., Zhang, S., Guo, G.C.: Phys. Rev. A 76 (01), 2334 (2007)ADSGoogle Scholar
  8. 8.
    Gerjuoy, E.: Phys. Rev. A 67 (05), 2308 (2003)ADSCrossRefGoogle Scholar
  9. 9.
    Ou, Y.C., Fan, H., Fei, S.M.: Phys. Rev. A 78 (01), 2311 (2008)MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    Li, X.S., Gao, X.H., Fei, S.M.: Phys. Rev. A 83, 034303 (2011)ADSCrossRefGoogle Scholar
  11. 11.
    Zhu, X.N., Fei, S.M. Phys. Rev. A 86, 054301 (2012)ADSCrossRefGoogle Scholar
  12. 12.
    Guo, Y., Hou, J.C., Wang, Y.C.: Quantum Inf. Process 12, 2641–2653 (2013)MathSciNetADSCrossRefMATHGoogle Scholar
  13. 13.
    Piani, M., Watrous, J.: Phys. Rev. Lett 102, 250501 (2009)MathSciNetADSCrossRefGoogle Scholar
  14. 14.
    Kostrikin, A.I.: Introduction to Algebra. Springer-Verlag, New York (1982)CrossRefGoogle Scholar
  15. 15.
    Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, Cambridge (1990)Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Robotics and Microsystems CenterSoochow UniversitySuzhouChina
  2. 2.School of Mechanical and Electric Engineering and Collaborative Innovation Center of Suzhou Nano Science and TechnologySoochow UniversitySuzhouChina
  3. 3.Department of MathematicsHarbin Institute of TechnologyHarbinChina

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