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Gaussian states that are invariant under partial anti-symplectic transformation are separable

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Abstract

It has been shown recently that Gaussian states that are invariant under partial transposition are separable states. In this paper, we define the class of anti-symplectic transformations and show that the transposition operation is a special case of the anti-symplectic transformation. As an extension of the existing result, we prove that Gaussian states that are invariant under partial anti-symplectic transformation are guaranteed to be separable.

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References

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  3. L.M. Duan, G. Giedke, J.I. Cirac, P. Zoller, Phys. Rev. Lett. 84, 2722 (2000)

    Article  ADS  Google Scholar 

  4. R. Simon, Phys. Rev. Lett. 84, 2726 (2000)

    Article  ADS  Google Scholar 

  5. P. Horodecki, M. Lewenstein, Phys. Rev. Lett. 85, 2657 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  6. A. Botero, B. Reznik, Phys. Rev. A 67, 052311 (2003)

    Article  ADS  Google Scholar 

  7. G. Adesso, A. Serafini, F. Illuminati, Phys. Rev. A 70, 022318 (2004)

    Article  ADS  Google Scholar 

  8. G. Adesso, Phys. Rev. Lett. 97, 130502 (2006)

    Article  ADS  Google Scholar 

  9. G. Adesso, F. Illuminati, J. Phys. A: Math. Theor. 40, 7821 (2007)

    Article  ADS  Google Scholar 

  10. P. Hyllus, J. Eisert, New J. Phys. 8, 51 (2006)

    Article  ADS  Google Scholar 

  11. S. Mancini, S. Severini, Electron. Notes Theor. Comput. Sci. 169, 121 (2007)

    Article  Google Scholar 

  12. L. Lami, C. Hirche, G. Adesso, A. Winter, Phys. Rev. Lett. 117, 220502 (2016)

    Article  ADS  Google Scholar 

  13. C. Weedbrook, S. Pirandola, R. García-Patrón, N.J. Cerf, T.C. Ralph, J.H. Shapiro, S. Lloyd, Rev. Mod. Phys. 84, 621 (2012)

    Article  ADS  Google Scholar 

  14. A. Belfakir, M. Ziane, M.E. Baz, Y. Hassouni, Eur. Phys. J. D 73, 216 (2019)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  16. R.F. Werner, M.M. Wolf, Phys. Rev. Lett. 86, 3658 (2001)

    Article  ADS  Google Scholar 

  17. K. Horodecki, M. Horodecki, P. Horodecki, J. Oppenheim, Phys. Rev. Lett. 94, 160502 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  18. R. Augusiak, P. Horodecki, Phys. Rev. A 80, 042307 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  19. C.J. Zhang, H. Nha, Y.S. Zhang, G.C. Guo, Phys. Rev. A 82, 032323 (2010)

    Article  ADS  Google Scholar 

  20. J. DiGuglielmo, A. Samblowski, B. Hage, C. Pineda, J. Eisert, R. Schnabel, Phys. Rev. Lett. 107, 240503 (2011)

    Article  ADS  Google Scholar 

  21. J. Zhang, Phys. Rev. A 83, 052327 (2011)

    Article  ADS  Google Scholar 

  22. F. Kaneda, R. Shimizu, S. Ishizaka, Y. Mitsumori, H. Kosaka, K. Edamatsu, Phys. Rev. Lett. 109, 040501 (2012)

    Article  ADS  Google Scholar 

  23. X. Jia, J. Zhang, Y. Wang, Y. Zhao, C. Xie, K. Peng, Phys. Rev. Lett. 108, 190501 (2012)

    Article  ADS  Google Scholar 

  24. T. Moroder, O. Gittsovich, M. Huber, O. Gühne, Phys. Rev. Lett. 113, 050404 (2014)

    Article  ADS  Google Scholar 

  25. S. Ma, M.J. Woolley, X. Jia, J. Zhang, Phys. Rev. A 100, 022309 (2019)

    Article  ADS  Google Scholar 

  26. S. Ma, S. Xue, Y. Guo, C.C. Shu, Quantum Inf. Process. 19, 225 (2020)

    Article  ADS  Google Scholar 

  27. S.L. Braunstein, P. van Loock, Rev. Mod. Phys. 77, 513 (2005)

    Article  ADS  Google Scholar 

  28. L. Lami, A. Serafini, G. Adesso, New J. Phys. 20, 023030 (2018)

    Article  ADS  Google Scholar 

  29. A. Serafini, G. Adesso, F. Illuminati, Phys. Rev. A 71, 032349 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  30. G. Giedke, B. Kraus, M. Lewenstein, J.I. Cirac, Phys. Rev. Lett. 87, 167904 (2001)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. School of Automation, Central South University, Changsha, 410083, P.R. China

    Shan Ma

  2. Peng Cheng Laboratory, Shenzhen, 518000, P.R. China

    Shan Ma

Authors
  1. Shan Ma
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Shan Ma conceived of the presented idea, and wrote the manuscript.

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Correspondence to Shan Ma.

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Ma, S. Gaussian states that are invariant under partial anti-symplectic transformation are separable. Eur. Phys. J. D 74, 172 (2020). https://doi.org/10.1140/epjd/e2020-10302-6

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  • DOI: https://doi.org/10.1140/epjd/e2020-10302-6

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