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A method for efficiently estimating non-Gaussianity of continuous-variable quantum states

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Abstract

We develop a method for efficiently calculating non-Gaussianity of quantum states in Wigner function representation based on the sine metric. In contradistinction to the known non-Gaussianity measures, we seek the corresponding reference Gaussian counterpart via the cumulant-expansion techniques of quantum state. We analyze this quantity for some non-Gaussian quantum states, which can not be well detected or quantified by other non-Gaussianity measures such as the degree of Gaussianity, the Hilbert-Schmidt metric and the relative entropy metric, thereby providing a good measure to quantify a genuine non-Gaussian state.

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References

  1. C.H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, W.K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).

    Article  ADS  MathSciNet  Google Scholar 

  2. R. Raussendorf, H.J. Briegel, Phys. Rev. Lett. 86, 5188 (2001).

    ADS  Google Scholar 

  3. N. Gisin, G. Ribordy, W. Tittel, H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).

    ADS  Google Scholar 

  4. T. Opatrný, G. Kurizki, D.G. Welsch, Phys. Rev. A 61, 032302 (2000).

    ADS  Google Scholar 

  5. S. Olivares, M.G.A. Paris, R. Bonifacio, Phys. Rev. A 67, 032314 (2003).

    ADS  Google Scholar 

  6. F. Dell’Anno, S. De Siena, L. Albano, F. Illuminati, Phys. Rev. A 76, 022301 (2007).

    ADS  Google Scholar 

  7. A. Mandilara, N.J. Cerf, Phys. Rev. A 86, 030102 (2012).

    ADS  Google Scholar 

  8. L. Lachman, R. Filip, Phys. Rev. A 88, 063841 (2013).

    ADS  Google Scholar 

  9. C. Hughes, M.G. Genoni, T. Tufarelli, M.G.A. Paris, M.S. Kim, Phys. Rev. A 90, 013810 (2014).

    ADS  Google Scholar 

  10. J. Park, J. Zhang, J. Lee, S.W. Ji, M. Um, D. Lv, K. Kim, H. Nha, Phys. Rev. Lett. 114, 190402 (2015).

    ADS  Google Scholar 

  11. J. Park, H. Nha, Phys. Rev. A 92, 062134 (2015).

    ADS  Google Scholar 

  12. A. Hertz, E. Karpov, A. Mandilara, N.J. Cerf, Phys. Rev. A 93, 032330 (2016).

    ADS  Google Scholar 

  13. I. Happ, M.A. Efremov, H. Nha, W.P. Schleich, New J. Phys. 20, 023046 (2018).

    ADS  Google Scholar 

  14. I. Happ, M.A. Efremov, H. Nha, W.P. Schleich, New J. Phys. 20, 039601 (2018).

    ADS  Google Scholar 

  15. M.G. Genoni, M.G.A. Paris, K. Banaszek, Phys. Rev. A 76, 042327 (2007).

    ADS  Google Scholar 

  16. M.G. Genoni, M.G.A. Paris, Phys. Rev. A 82, 052341 (2010).

    ADS  Google Scholar 

  17. J.S. Ivan, M.S. Kumar, R. Simon, Quantum Inf. Process. 11, 853 (2012).

    MathSciNet  Google Scholar 

  18. M.G. Genoni, M.G.A. Paris, K. Banaszek, Phys. Rev. A 78, 060303 (2008).

    ADS  MathSciNet  Google Scholar 

  19. P. Marian, T.A. Marian, Phys. Rev. A 88, 012322 (2013).

    ADS  Google Scholar 

  20. J. Park, J. Lee, K. Baek, S.W. Ji, H. Nha, Phys. Rev. A 100, 012333 (2019).

    ADS  Google Scholar 

  21. I. Ghiu, P. Marian, T.A. Marian, Phys. Scr. T153, 014028 (2013).

    ADS  Google Scholar 

  22. M.S. Figueira, M.E. Foglio, G.G. Martinez, Phys. Rev. B 50, 17933 (1994).

    ADS  Google Scholar 

  23. W. Kutzelnigg, D. Mukherjee, J. Chem. Phys. 110, 2800 (1999).

    ADS  Google Scholar 

  24. A. Rodriguez, C. Tsallis, J. Math. Phys. 51, 073301 (2010).

    ADS  MathSciNet  Google Scholar 

  25. D. Bures, Trans. Am. Math. Soc. 135, 199 (1969).

    Google Scholar 

  26. P. Marian, T.A. Marian, H. Scutaru, Phys. Rev. A 68, 062309 (2003).

    ADS  Google Scholar 

  27. P. Marian, T.A. Marian, Phys. Rev. A 77, 062319 (2008).

    ADS  Google Scholar 

  28. P. Marian, T.A. Marian, H. Scutaru, Phys. Rev. Lett. 88, 153601 (2002).

    ADS  Google Scholar 

  29. D. Spehner, M. Orszag, New J. Phys. 15, 103001 (2013).

    ADS  MathSciNet  Google Scholar 

  30. A. Gilchrist, N.K. Langford, M.A. Nielsen, Phys. Rev. A 71, 062310 (2005).

    ADS  Google Scholar 

  31. J.A. Miszczak, Z. Puchala, P. Horodecki, A. Uhlmann, K. Zczkowski, Quantum Inf. Comput. 9, 0103 (2009).

    MathSciNet  Google Scholar 

  32. GhS Paraoanu, H. Scutaru, Phys. Rev. A 61, 022306 (2000).

    ADS  Google Scholar 

  33. V. Dodonov, I. Malkin, V. Man’ko, Physica 72, 597 (1974).

    ADS  MathSciNet  Google Scholar 

  34. V. Bužek, A. Vidiella-Barranco, P.L. Knight, Phys. Rev. A 45, 6570 (1992).

    ADS  Google Scholar 

  35. Y.J. Xia, G.C. Guo, Phys. Lett. A 136, 281 (1989).

    ADS  Google Scholar 

  36. F.L. Li, H.R. Li, J.X. Zhang, S.Y. Zhu, Phys. Rev. A 66, 024302 (2002).

    ADS  MathSciNet  Google Scholar 

  37. Y.W. Cheong, H. Kim, H.W. Lee, Phys. Rev. A 70, 032327 (2004).

    ADS  Google Scholar 

  38. M. Heid, N. Lütkenhaus, Phys. Rev. A 76, 022313 (2007).

    ADS  Google Scholar 

  39. W. Vogel, J. Sperling, Phys. Rev. A 89, 052302 (2014).

    ADS  Google Scholar 

  40. H. Jeong, N.B. An, Phys. Rev. A 74, 022104 (2006).

    ADS  MathSciNet  Google Scholar 

  41. F. Albarelli, M.G. Genoni, M.G.A. Paris, A. Ferraro, Phys. Rev. A 98, 052350 (2018).

    ADS  Google Scholar 

  42. G.S. Agarwal, K. Tara, Phys. Rev. A 46, 485 (1992).

    ADS  Google Scholar 

  43. A. Zavatta, V. Parigi, M. Bellini, Phys. Rev. A 75, 052106 (2007).

    ADS  Google Scholar 

  44. R. Filip, L. Mišta Jr, Phys. Rev. Lett. 106, 200401 (2011).

    ADS  Google Scholar 

  45. M. Ježek, I. Straka, M. Mičuda, M. Dušek, J. Fiurášek, R. Filip, Phys. Rev. Lett. 107, 213602(2011) .

    ADS  Google Scholar 

  46. M. Barbieri, N. Spagnolo, M.G. Genoni, F. Ferreyrol, R. Blandino, M.G.A. Paris, P. Grangier, R. Tualle-Brouri, Phys. Rev. A 82, 063833 (2010).

    ADS  Google Scholar 

  47. A. Allevi, S. Olivares, M. Bondani, Opt. Exp. 20, 24850 (2012).

    ADS  Google Scholar 

  48. A. Allevi, S. Olivares, M. Bondani, Int. J. Quantum Inf. 10, 1241006 (2012).

    Google Scholar 

  49. D.E. Browne, J. Eisert, S. Scheel, M.B. Plenio, Phys. Rev. A 67, 062320 (2003).

    ADS  Google Scholar 

  50. C. Oh, C. Lee, L. Banchi, S.Y. Lee, C. Rockstuhl, H. Jeong, Phys. Rev. A 100, 012323 (2019).

    ADS  Google Scholar 

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Authors and Affiliations

  1. College of Electrical and Information Engineering, Huaihua University, Huaihua, 418008, P.R. China

    Shao-Hua Xiang & Cheng Xiang

  2. College of Mechanical, Optoelectronics and Physics, Huaihua University, Huaihua, 418008, P.R. China

    Shao-Hua Xiang, Yu-Jing Zhao, Wei Wen & Xue-Wen Long

Authors
  1. Shao-Hua Xiang
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  2. Yu-Jing Zhao
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  3. Cheng Xiang
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  4. Wei Wen
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  5. Xue-Wen Long
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Correspondence to Shao-Hua Xiang.

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Xiang, SH., Zhao, YJ., Xiang, C. et al. A method for efficiently estimating non-Gaussianity of continuous-variable quantum states. Eur. Phys. J. D 74, 16 (2020). https://doi.org/10.1140/epjd/e2019-100421-6

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  • DOI: https://doi.org/10.1140/epjd/e2019-100421-6

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