Skip to main content
Log in

Detecting nonclassicality via Gaussian noise channel

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

By exploiting the decoherent effect of Gaussian noise channel, we formulate a simple approach to quantifying optical nonclassicality of an optical state in terms of Wick-ordered characteristic function. We present a family of quantifiers of single-mode bosonic nonclassicality, which have many desirable properties. We further illustrate the quantifiers by several typical states. Our approach can also be generalized to the multi-mode cases.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

Data Availability Statement

This manuscript has no associated data.

References

  1. S. Haroche, J.M. Raimond, Exploring the quantum (Oxford University Press, Oxford, 2006)

    Book  MATH  Google Scholar 

  2. V.V. Dodonov, V.I. Manko, Theory of nonclassical states of light (Taylor and Francis, London, 2003)

    Book  Google Scholar 

  3. S. Haroche, Controlling photons in a box and exploring the quantum to classical boundary. Rev. Mod. Phys. 85, 1083 (2013)

    Article  ADS  Google Scholar 

  4. D.J. Wineland, Superposition, entanglement, and raising Schrödinger’s cat. Rev. Mod. Phys. 85, 1103 (2013)

    Article  ADS  Google Scholar 

  5. R.J. Glauber, Coherent and incoherent states of the radiation field. Phys. Rev. 131, 2766 (1963)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. E.C.G. Sudarshan, Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams. Phys. Rev. Lett. 10, 277 (1963)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. U.M. Titulaer, R.J. Glauber, Correlation functions for coherent fields. Phys. Rev. 140, B676 (1965)

    Article  ADS  MathSciNet  Google Scholar 

  8. H.J. Kimble, M. Dagenais, L. Mandel, Photon antibunching in resonance fluorescence. Phys. Rev. Lett. 39, 691 (1977)

    Article  ADS  Google Scholar 

  9. L. Mandel, Sub-Poissonian photon statistics in resonance fluorescence. Opt. Lett. 4, 205 (1979)

    Article  ADS  Google Scholar 

  10. M. Hillery, Nonclasssical distance in quantum optics. Phys. Rev. A 35, 725 (1987)

    Article  ADS  Google Scholar 

  11. C.T. Lee, Measure of the nonclassicality of nonclassical states. Phys. Rev. A 44, R2775 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  12. D.F. Walls, G.J. Milburn, Quantum optics (Springer, Berlin, 1994)

    Book  MATH  Google Scholar 

  13. M.O. Scully, M.S. Zubairy, Quantum optics (Cambridge University Press, Cambridge, 1997)

    Book  Google Scholar 

  14. U. Leonhardt, Measuring the quantum state of light (Cambridge University Press, Cambridge, 1997)

    MATH  Google Scholar 

  15. W. Vogel, Nonclassical states: an observable criterion. Phys. Rev. Lett. 84, 1849 (2000)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Th. Richter, W. Vogel, Nonclassicality of quantum states: A hierarchy of observable conditions. Phys. Rev. Lett. 89, 283601 (2002)

    Article  ADS  Google Scholar 

  17. P. Marian, T.A. Marian, H. Scutaru, Quantifying nonclassicality of one-mode Gaussian states of the radiation field. Phys. Rev. Lett. 88, 153601 (2002)

    Article  ADS  Google Scholar 

  18. M.S. Kim, W. Son, V. Buzek, P.L. Knight, Entanglement by a beam splitter: nonclassicality as a prerequisite for entanglement. Phys. Rev. A 65, 032323 (2002)

    Article  ADS  Google Scholar 

  19. X. Wang, Theorem for the beam-splitter entangler. Phys. Rev. A 66, 024303 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  20. J.M.C. Malbouisson, B. Baseia, On the measure of nonclassicality of field states. Phys. Scr. 67, 93 (2003)

    Article  ADS  MATH  Google Scholar 

  21. A. Kenfack, K. Życzkowski, Negativity of the Wigner function as an indicator of non-classicality. J. Opt. B Quantum Semiclass. Opt. 6, 396 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  22. J.K. Asbóth, J. Calsamiglia, H. Ritsch, Computable measure of nonclassicality for light. Phys. Rev. Lett. 94, 173602 (2005)

    Article  ADS  Google Scholar 

  23. Th. Richter, W. Vogel, Nonclassical characteristic functions for highly sensitive measurements. Phys. Rev. A 76, 053835 (2007)

    Article  ADS  Google Scholar 

  24. T. Kiesel, W. Vogel, Nonclassicality filters and quasiprobabilities. Phys. Rev. A 82, 032107 (2010)

    Article  ADS  Google Scholar 

  25. A. Mari, K. Kieling, B.M. Nielsen, E.S. Polzik, J. Eisert, Directly estimating nonclassicality. Phys. Rev. Lett. 106, 010403 (2011)

    Article  ADS  Google Scholar 

  26. C. Gehrke, J. Sperling, W. Vogel, Quantification of nonclassicality. Phys. Rev. A 86, 052118 (2012)

    Article  ADS  Google Scholar 

  27. J. Sperling, W. Vogel, Convex ordering and quantification of quantumness. Phys. Scr. 90, 074024 (2015)

    Article  ADS  Google Scholar 

  28. S. Ryl, J. Sperling, W. Vogel, Quantifying nonclassicality by characteristic funtions. Phys. Rev. A 95, 053825 (2017)

    Article  ADS  Google Scholar 

  29. B. Yadin, F.C. Binder, J. Thompson, V. Narasimhachar, M. Gu, M.S. Kim, Operational resource theory of continuous-variable nonclassicality. Phys. Rev. X 8, 041038 (2018)

    Google Scholar 

  30. K.C. Tan, H. Jeong, Nonclassical light and metrological power: an introductory review. AVS Quantum Sci. 1, 014701 (2019)

    Article  ADS  Google Scholar 

  31. S. de Bièvre, D.B. Horoshko, G. Patera, M.I. Kolobov, Measuring nonclassicality of Bosonic field quantum states via operator ordering sensitivity. Phys. Rev. Lett. 122, 080402 (2019)

    Article  Google Scholar 

  32. S. Luo, Y. Zhang, Quantifying nonclassicality via Wigner-Yanase skew information. Phys. Rev. A 100, 032116 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  33. W. Ge, K. Jacobs, S. Asiri, M. Foss-Feig, M.S. Zubairy, Operational resource theory of nonclassicality via quantum metrology. Phys. Rev. Res. 2, 023400 (2020)

    Article  Google Scholar 

  34. M. Bohmann, E. Agudelo, Phase-space inequalities beyond negativities. Phys. Rev. Lett. 124, 133601 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  35. M. Bohmann, E. Agudelo, J. Sperling, Probing nonclassicality with matrices of phase-space distributions. Quantum 4, 343 (2020)

    Article  Google Scholar 

  36. S. Luo, Y. Zhang, Quantumness of Bosonic field states. Int. J. Theor. Phys. 59, 206 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  37. Y. Zhang, S. Luo, Quantum states as observables: Their variance and nonclassicality. Phys. Rev. A 102, 062211 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  38. K.C. Tan, S. Choi, H. Jeong, Negativity of quasiprobability distributions as a measure of nonclassicality. Phys. Rev. Lett. 124, 110404 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  39. B. Kühn, W. Vogel, V. Thiel, S. Merkouche, B.J. Smith, Gaussian versus non-Gaussian filtering of phase-insensitive nonclassicality. Phys. Rev. Lett. 126, 173603 (2021)

    Article  ADS  Google Scholar 

  40. V. Biagi, M. Bohmann, E. Agudelo, M. Bellini, A. Zavatta, Experimental certification of nonclassicality via phase-space inequalities. Phys. Rev. Lett. 126, 023605 (2021)

    Article  ADS  Google Scholar 

  41. J. Park, J. Lee, H. Nha, Verifying single-mode nonclassicality beyond negativity in phase space. Phys. Rev. Research 3, 043116 (2021)

    Article  ADS  Google Scholar 

  42. S. Fu, S. Luo, Y. Zhang, On non-convexity of the nonclassicality measure via operator ordering sensitivity. Front. Phys. 10, 955786 (2022)

    Article  Google Scholar 

  43. S. Bochner, Monotone funktionen, Stieltjessche integrale und harmonische analyse. Math. Ann. 108, 378 (1933)

    Article  MathSciNet  MATH  Google Scholar 

  44. A. Perelomov, Generalized coherent states and their applications (Springer, Berlin, 1986)

    Book  MATH  Google Scholar 

  45. K. Cahill, R.J. Glauber, Ordered expansions in boson amplitude operators. Phys. Rev. 177, 1857 (1969)

    Article  ADS  Google Scholar 

  46. K. Cahill, R.J. Glauber, Density operators and quasiprobability distributions. Phys. Rev. 177, 1882 (1969)

    Article  ADS  Google Scholar 

  47. H. Yuen, V.W.S. Chan, Noise in homodyne and heterodyne detection. Opt. Lett. 8, 177 (1983)

    Article  ADS  Google Scholar 

  48. S. Ryl, J. Sperling, E. Agudelo, M. Mraz, S. Köhnke, B. Hage, W. Vogel, Unified nonclassicality criteria. Phys. Rev. A 92, 011801(R) (2015)

    Article  ADS  Google Scholar 

  49. C. Flühmann, J.P. Home, Direct characteristic-function tomography of quantum states of the trapped-ion motional oscillator. Phys. Rev. Lett. 125, 043602 (2020)

    Article  ADS  Google Scholar 

  50. K.S. Gibbons, M.J. Hoffman, W.K. Wootters, Discrete phase space based on finite fields. Phys. Rev. A 70, 062101 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  51. D. Gross, Hudson’s theorem for finite-dimensional quantum systems. J. Math. Phys. 47, 122107 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  52. C. Ferrie, J. Emerson, Framed Hilbet space: hanging the quasi-probability pictures of quantum theory. New. J. Phys. 11, 063040 (2009)

    Article  ADS  Google Scholar 

  53. D. Gross, Non-negative Wigner functions in prime dimensions. Appl. Phys. B 86, 367 (2007)

    Article  ADS  Google Scholar 

  54. C. Ferrie, Quasi-probability representations of quantum theory with applications to quantum information science. Rep. Prog. Phys. 74, 116001 (2011)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  56. A.S. Holevo, V. Giovannetti, Quantum channels and their entropic characteristics. Rep. Prog. Phys. 75, 046001 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  57. G. Lachs, Theoretical aspects of mixtures of thermal and coherent radiation. Phys. Rev. 138, B1012 (1965)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  58. G.M. D’Ariano, P. Lo Presti, Imprinting complete information about a quantum channel on its output state. Phys. Rev. Lett. 91, 047902 (2003)

    Article  ADS  Google Scholar 

  59. A.S. Holevo, Quantum systems, channels, information (De Gruyter, Berlin, 2012)

    Book  MATH  Google Scholar 

  60. M.J.W. Hall, M.J. O’Rourke, Realistic performance of the maximum information channel. Quantum Opt. 5, 161 (1993)

    Article  ADS  Google Scholar 

  61. M.J.W. Hall, Gaussian noise and quantum-optical communication. Phys. Rev. A 50, 3295 (1994)

    Article  ADS  Google Scholar 

  62. M.S. Kim, F.A.M. de Oliveira, P.L. Knight, Properties of squeezed number states and squeezed thermal states. Phys. Rev. A 40, 2494 (1989)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Key R &D Program of China, Grant No. 2020YFA0712700, and the National Natural Science Foundation of China, Grant No. 11875317.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yue Zhang.

Ethics declarations

Conflict of interest

There is no conflict of interest.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, X., Luo, S. & Zhang, Y. Detecting nonclassicality via Gaussian noise channel. Eur. Phys. J. Plus 137, 1382 (2022). https://doi.org/10.1140/epjp/s13360-022-03594-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-022-03594-7

Navigation