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Separable State Decompositions for a Class of Mixed States

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Abstract

We study certain quantum states for which the PPT criterion is both sufficient and necessary for separability. A class of n×n bipartite mixed states is presented and the conditions of PPT for these states are derived. The separable pure state decompositions of these states are explicitly constructed when they are PPT.

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References

  1. Preskill, J.: The theory of quantum information and quantum computation. California Inst. of Tech. (2000). http://www.theory.caltech.edu/people/preskill/ph229/

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

    MATH  Google Scholar 

  3. Bouwmeester, D., Ekert, A., Zeilinger, A. (eds.): The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation and Quantum Commutation. Springer, New York (2000)

    Google Scholar 

  4. Bell, J.S.: Physics (N.Y.) 1, 195 (1964)

    Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Horodecki, M., Horodecki, P.: Phys. Rev. A 59, 4206 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  7. Cerf, N.J., Adami, C., Gingrich, R.M.: Phys. Rev. A 60, 898 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  8. Nielsen, M.A., Kempe, J.: Phys. Rev. Lett. 86, 5184 (2001)

    Article  ADS  Google Scholar 

  9. Terhal, B.: Phys. Lett. A 271, 319 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. Lewenstein, M., Kraus, B., Cirac, J.I., Horodecki, P.: Phys. Rev. A 62, 052310 (2000)

    Article  ADS  Google Scholar 

  11. Rudolph, O.: Phys. Rev. A 67, 032312 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  12. Chen, K., Wu, L.A.: Phys. Lett. A 306, 14 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. Albeverio, S., Chen, K., Fei, S.M.: Phys. Rev. A 68, 062313 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  14. Horodecki, P.: Phys. Lett. A 232, 333–339 (1997)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. Hofmann, H.F., Takeuchi, S.: Phys. Rev. A 68, 032103 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  16. Gühne, O., Mechler, M., Töth, G., Adam, P.: Phys. Rev. A 74, 010301(R) (2006)

    Article  Google Scholar 

  17. Gühne, O.: Phys. Rev. Lett. 92, 117903 (2004)

    Article  ADS  Google Scholar 

  18. Zhang, C.J., Zhang, Y.S., Zhang, S., Guo, G.C.: Phys. Rev. A 76, 012334 (2007)

    Article  ADS  Google Scholar 

  19. Vicente, J.D.: Quantum Inf. Comput. 7, 624 (2007)

    MathSciNet  MATH  Google Scholar 

  20. Vicente, J.D.: J. Phys. A, Math. Theor. 41, 065309 (2008)

    Article  ADS  Google Scholar 

  21. Gühne, O., Hyllus, P., Gittsovich, O., Eisert, J.: Phys. Rev. Lett. 99, 130504 (2007)

    Article  MathSciNet  Google Scholar 

  22. Horodecki, P., Lewenstein, M., Vidal, G., Cirac, I.: Phys. Rev. A 62, 032310 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  23. Albeverio, S., Fei, S.M., Goswami, D.: Phys. Lett. A 286, 91 (2001)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  24. Fei, S.M., Gao, X.H., Wang, X.H., Wang, Z.X., Wu, K.: Phys. Lett. A 300, 555 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  25. Wootters, W.K.: Phys. Rev. Lett. 80, 2245 (1998)

    Article  ADS  Google Scholar 

  26. Horodecki, M., Horodecki, P., Horodecki, R.: Phys. Lett. A 233, 1 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  27. Horodecki, P., Lewenstein, M., Vidal, G., Cirac, I.: Phys. Rev. A 62, 032310 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  28. Fei, S.M., Li-Jost, X.: Int. J. Quantum Inf. 7, 587 (2009)

    Article  MATH  Google Scholar 

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Acknowledgements

Huang gratefully acknowledges the grant support from the Natural Sciences Foundation for Hainan Province 111006. Jing is grateful for the support of Simons Foundation grant 198129 and NSFC grant 11271138 during the work. This work is also supported by the NSFC under number 11105226. We would like to acknowledge helpful discussions with Bobo Hua.

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Authors and Affiliations

  1. Max-Planck-Institute for Mathematics in the Sciences, Leipzig, 04103, Germany

    Ting-Gui Zhang, Xianqing Li-Jost & Shao-Ming Fei

  2. School of Mathematics and Statistics, Hainan Normal University, Haikou, 571158, China

    Xiaofen Huang

  3. School of Sciences, South China University of Technology, Guangzhou, 510640, China

    Naihuan Jing

  4. Department of Mathematics, North Carolina State University, Raleigh, NC, 27695, USA

    Naihuan Jing

  5. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China

    Shao-Ming Fei

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  1. Ting-Gui Zhang
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  2. Xiaofen Huang
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  3. Xianqing Li-Jost
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  4. Naihuan Jing
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  5. Shao-Ming Fei
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Correspondence to Xiaofen Huang.

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Zhang, TG., Huang, X., Li-Jost, X. et al. Separable State Decompositions for a Class of Mixed States. Int J Theor Phys 52, 4148–4154 (2013). https://doi.org/10.1007/s10773-013-1727-8

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  • DOI: https://doi.org/10.1007/s10773-013-1727-8

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