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Hidden Correlations and Information-Entropic Inequalities in Systems of Qudits†

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Journal of Russian Laser Research Aims and scope

Abstract

We present the results of our study of correlations in noncomposite systems like qudits (N-level atom or spin-j system). We show that they correspond to correlations in composite systems like bipartite or multipartite systems. We establish the correspondence between correlations in noncomposite systems and composite ones using the map of indices labeling the random variables in classical probability theory or matrix elements of density matrices in quantum mechanics. We obtain new information-entropic inequalities for density matrices of noncomposite systems. Also we present Bayes’ formula for noncomposite classical system with one random variable. Finally we discuss the possibility to use hidden correlations and entanglement of a single-qudit state.

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References

  1. M. A. Man’ko and V. I. Man’ko, J. Russ. Laser Res., 34, 203 (2013).

    Google Scholar 

  2. M. A. Man’ko and V. I. Man’ko, Phys. Scr., T160, 014030 (2014).

    ADS  Google Scholar 

  3. M. A. Man’ko and V. I. Man’ko, Int. J. Quantum Inf., 12, 156006 (2014).

    Google Scholar 

  4. M. A. Man’ko and V. I. Man’ko, J. Russ. Laser Res., 35 298 (2014).

    Google Scholar 

  5. M. A. Man’ko and V. I. Man’ko, Entropy, 17, 2876 (2015).

    ADS  MathSciNet  Google Scholar 

  6. M. A. Man’ko and V. I. Man’ko, J. Russ. Laser Res., 36, 301 (2015).

    Google Scholar 

  7. M. A. Man’ko, V. I. Man’ko, and G. Marmo, Nuovo Cimento C, 38, iss. 5, paper 167 (2015).

  8. J. A. Lopez-Saldivar, O. Castaños, M. A. Man’ko, and V. I. Man’ko, Entropy, 21(8), 736 (2019).

    ADS  Google Scholar 

  9. M. A. Man’ko and V. I. Man’ko, J. Russ. Laser Res., 37, 1 (2016).

    Google Scholar 

  10. M. A. Man’ko and V. I. Man’ko, J. Russ. Laser Res., 38, 211 (2017).

    Google Scholar 

  11. M. A. Man’ko and V. I. Man’ko, J. Russ. Laser Res., 39, 1 (2018).

    Google Scholar 

  12. M. A. Man’ko and V. I. Man’ko, Phys. Scr., 93, 084002 (2018).

    ADS  Google Scholar 

  13. J. A. Lopez-Saldivar, O. Castaños, E. Nahmad-Achar, et al., Entropy, 20(9), 630 (2018).

    ADS  Google Scholar 

  14. M. A. Man’ko and V. I. Man’ko, Entropy, 20(9), 692 (2018).

    ADS  Google Scholar 

  15. P. A. M. Dirac, The Principles of Quantum Mechanics, Clarendon Press, Oxford, UK (1981).

  16. E. Schrödinger, Ann. Phys., 384, 361; 489 (1926).

    ADS  MATH  Google Scholar 

  17. L. Landau, Z. Phys., 45, 430 (1927).

    ADS  Google Scholar 

  18. J. von Neumann, Gött. Nach., 1, 245 (1927).

    Google Scholar 

  19. S. Mancini, V. I. Man’ko, and P. Tombesi, Phys. Lett. A, 213, 1 (1996).

    ADS  MathSciNet  Google Scholar 

  20. V. V. Dodonov and V. I. Man’ko, Phys. Lett. A, 229, 335 (1997).

    ADS  MathSciNet  Google Scholar 

  21. M. Asorey, A. Ibort, G. Marmo, and F. Ventriglia, Phys. Scr., 90, 074031 (2015).

    ADS  Google Scholar 

  22. D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, Phys. Rev. Lett., 70, 1244 (1993).

    ADS  Google Scholar 

  23. J. Bertrand and P. Bertrand, Found. Phys., 17, 397 (1987).

    ADS  MathSciNet  Google Scholar 

  24. K. Vogel and H. Risken, Phys. Rev. A, 40, 2847 (1989).

    ADS  Google Scholar 

  25. A. I. Lvovsky and M. G. Raymer, Rev. Mod. Phys., 81, 299 (2009).

    ADS  Google Scholar 

  26. R. J. Glauber, Phys. Rev. Lett., 10, 84 (1963).

    ADS  MathSciNet  Google Scholar 

  27. E. C. G. Sudarshan, Phys. Rev. Lett., 10, 277 (1963).

    ADS  MathSciNet  Google Scholar 

  28. E. C. G. Sudarshan, P. M. Mathews, and Jayaseetha Rau, Phys. Rev., 121, 920 (1961).

    ADS  MathSciNet  MATH  Google Scholar 

  29. K. Kraus, States, Effects and Operations, Springer, Berlin (1988).

  30. V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, J. Math. Phys., 17, 821 (1976).

    Article  ADS  Google Scholar 

  31. G. Lindblad, Commun. Math. Phys., 48, 119 (1976).

    Article  ADS  Google Scholar 

  32. E. Wigner, Phys. Rev., 40, 749 (1932).

    ADS  Google Scholar 

  33. K. Husimi, Proc. Phys. Math. Soc. Jpn., 22, 264 (1940).

    Google Scholar 

  34. Y. J. Kano, J. Math. Phys., 6, 1913 (1965).

    ADS  Google Scholar 

  35. R. Glauber and V. I. Man’ko, “Damping and fluctuations in the systems of two entangled quantum oscillators,” in: Group Theory, Gravitation, and Physics of Elementary Particles, Proceedings of the Lebedev Physical Institute [in Russian], Nauka, Moscow (1986), Vol. 167 [English translation by Nova Science, Commack, New York (1987), Vol. 167].

  36. R. Glauber and V. I. Man’ko, Zh. Éksp. Teor. Fiz., 87, 790 (1984) [Sov. Phys. JETP, 60, 450 (1984)].

  37. G. Schrade, V. I. Man’ko, W. P. Schleich, and R. Glauber, Quantum Semiclass. Opt., 7, 307 (1995).

    ADS  Google Scholar 

  38. V. I. Man’ko and O. V. Man’ko, J. Exp. Theor. Phys., 85, 430 (1997).

    ADS  Google Scholar 

  39. V. N. Chernega, O. V. Man’ko, and V. I. Man’ko, J. Russ. Laser Res., 35, 278 (2014).

    Google Scholar 

  40. E. C. G. Sudarshan, J. Russ. Laser Res., 24, 195 (2003).

    Google Scholar 

  41. V. I. Man’ko, G. Marmo, E. C. G. Sudarshan, and F. Zaccaria, J. Russ. Laser Res., 20, 421 (1999).

    Google Scholar 

  42. V. I. Man’ko, G. Marmo, E. C. G. Sudarshan, and F. Zaccaria, J. Russ. Laser Res., 21, 305 (2000).

    Google Scholar 

  43. V. I. Man’ko, G. Marmo, E. C. G. Sudarshan, and F. Zaccaria, J. Russ. Laser Res., 24, 507 (2003).

    Google Scholar 

  44. J. Klauder and E. C. G. Sudarshan, Foundation of Quantum Optics, Russin translation, Mir, Moscow (1970).

  45. M. A. Man’ko, V. I. Man’ko, G. Marmo, et al., “Dichotomic probability representation of quantum states,” arXiv:1905.10561 quant-ph (submitted to J. Phys. A: Math. Theor., 2019).

  46. A. N. Kolmogorov, Foundation of the Theory of Probability, Chelsea, New York (1956).

  47. A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory, North Holland, Amsterdam (1982).

  48. Albert N. Shiryaev, Probability-1, Springer, Berlin, Germany (2016).

  49. A. Khrennikov, Probability and Randomness. Quantum versus Classical, World Scientific, Singapore (2016).

  50. V. I. Man’ko and Zh. Zeilov, J. Russ. Laser Res., 38 50 (2017).

    Google Scholar 

  51. V. N. Chernega, O. V. Man’ko, and V. I. Man’ko, J. Russ. Laser Res., 38, 141 (2017).

    Google Scholar 

  52. V. N. Chernega, O. V. Man’ko, and V. I. Man’ko, J. Russ. Laser Res., 38, 324 (2017).

    Google Scholar 

  53. V. N. Chernega, O. V. Man’ko, and V. I. Man’ko, J. Russ. Laser Res., 38, 416 (2017).

    Google Scholar 

  54. V. N. Chernega, O. V. Man’ko, and V. I. Man’ko, J. Phys. Conf. Ser., 1071, 012008 (2018).

  55. V. N. Chernega, O. V. Man’ko, and V. I. Man’ko, J. Russ. Laser Res., 39, 128 (2018).

    Google Scholar 

  56. M. A. Man’ko, J. Phys.: Conf. Ser., 1071, 012015 (2018).

  57. J. A. Lopez-Saldivar, O. Casta˜nos, M. A. Man’ko, and V. I. Man’ko, Physica A, 491, 64 (2018).

  58. J. A. Lopez-Saldivar, O. Castaños, M. A. Man’ko, and V. I. Man’ko, Phys. Rev. E, 97, 022128 (2018).

  59. V. I. Man’ko, G. Marmo, F. Ventriglia, and P. Vitale, J. Phys. A: Math. Theor., 50, 335302 (2017).

    Google Scholar 

  60. V. N. Chernega, O. V. Man’ko, and V. I. Man’ko, Eur. Phys. J. D, 73, 10 (2019); DOI: https://doi.org/10.1140/epjd/e2018-90487-9.

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Authors and Affiliations

  1. Lebedev Physical Institute, Russian Academy of Sciences, Leninskii Prospect 53, Moscow, 119991, Russia

    Igor Ya. Doskoch & Margarita A. Man’ko

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  1. Igor Ya. Doskoch
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  2. Margarita A. Man’ko
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Correspondence to Margarita A. Man’ko.

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Doskoch, I.Y., Man’ko, M.A. Hidden Correlations and Information-Entropic Inequalities in Systems of Qudits†. J Russ Laser Res 40, 293–312 (2019). https://doi.org/10.1007/s10946-019-09805-4

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  • DOI: https://doi.org/10.1007/s10946-019-09805-4

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