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Conditional Information and Hidden Correlations in Single-qudit States

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Journal of Russian Laser Research Aims and scope

Abstract

We discuss the notions of mutual information and conditional information for noncomposite systems, classical and quantum; both the mutual information and the conditional information are associated with the presence of hidden correlations in the state of a single qudit. We consider analogs of the entanglement phenomena in the systems without subsystems related to strong hidden quantum correlations.

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References

  1. A. N. Kolmogorov, Foundations of the Theory of Probability, 2nd ed., Chelsea Publishing Company, New York (1956).

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  3. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, UK (2000).

    MATH  Google Scholar 

  4. L. D. Landau, Z. Phys., 45, 430 (1927).

    Article  ADS  Google Scholar 

  5. J. von Neumann, Göttingenische Nachrichten, 11 (Nov. 1927), S. 245–272.

  6. J. von Neumann, Mathematische Grundlagen der Quantummechanik, Springer, Berlin (1932).

    Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  9. M. A. Man’ko, Phys. Scr., T153, 014045 (2013).

    Article  ADS  Google Scholar 

  10. M. A. Man’ko and V. I. Man’ko, J. Phys.: Conf. Ser., 442, 012008 (2013).

    Google Scholar 

  11. M. A. Man’ko, V. I. Man’ko, G. Marmo, et al., Nuovo Cimento C, 36, 163 (2013).

    Google Scholar 

  12. M. A. Man’ko and V. I. Man’ko, J. Phys.: Conf. Ser., 538, 012016 (2014).

    Google Scholar 

  13. M. A. Man’ko and V. I. Man’ko, J. Russ. Laser Res., 35, 509 (2014).

    Article  Google Scholar 

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

    Google Scholar 

  15. P. Adam, V. A. Andreev, J. Janszky, et al., Phys. Scr., T160, 014001 (2014).

    Article  ADS  Google Scholar 

  16. M. A. Man’ko, V. I. Man’ko, G. Marmo, et al., J. Russ. Laser Res., 35, 79 (2014).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  19. M. A. Man’ko and V. I. Man’ko, J. Russ. Laser Res., 35, 509 (2014)

    Article  Google Scholar 

  20. M. A. Man’ko and V. I. Man’ko, J. Russ. Laser Res., 35, 582 (2014).

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  23. M. A. Man’ko and V. I. Man’ko, J. Phys.: Conf. Ser., 698, 012004 (2016).

    Google Scholar 

  24. M. A. Man’ko, V. I. Man’ko, and G. Marmo, Nuovo Cimento C, 38, 167 (2016).

    ADS  Google Scholar 

  25. A. A. Klyachko, M. A. Can, S. Binicioˇglu, and A. S. Shumovsky, Phys. Rev. Lett., 101, 020403 (2008).

    Article  ADS  MathSciNet  Google Scholar 

  26. A. Figueroa, J. Lopez, O. Casta˜nos, et al., J. Phys. A: Math. Theor., 48, 065301 (2015).

    Article  ADS  Google Scholar 

  27. M. Horodecki and J. Oppenheim, Nature Commun., 4, 2059 (2013).

    Article  ADS  Google Scholar 

  28. J. Goold, M. Huber, A. Riera, et al., J. Phys. A: Math. Theor., 49, 143001 (2016).

    Article  ADS  Google Scholar 

  29. J. A. López-Saldívar, O. Castaños, M. A. Man’ko, and V. I. Man’ko, “New entropic inequalities for qubit and unimodal Gaussian states,” Eur. Phys. Lett. (2017, submitted).

  30. P. Facchi, G. Garnero, and M. Ligabo, “Quantum fluctuation relations,” arXiv:1705.06096 [quantph].

  31. P. Facchi and G. Garnero, “Quantum thermodynamics and canonical typicality,” arXiv:1705.02270 [quant-ph].

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

    Article  Google Scholar 

  33. V. N. Chernega, O. V. Man’ko, V. I. Man’ko, and Zh. Seilov, “New information and entropic inequalities for Clebsch–Gordan coefficients,” arXiv:1606.00854v4 [quant-ph]; Theor. Math. Phys. (2017, in press).

  34. A. D. Pasquale, “Bipartite entanglement of large quantum systems,” arXiv:1206.6749v2 [quant-ph].

  35. A. D. Pasquale, P. Facchi, V. G. Giovannetti, et al., J. Phys. A: Math. Theor., 45, 015308 (2012).

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  38. A. K. Fedorov, E. O. Kiktenko, O. V. Man’ko, and V. I. Man’ko, Phys. Rev. A, 91, 042312 (2015).

    Article  ADS  Google Scholar 

  39. E. O. Kiktenko, A. K. Fedorov, A. A. Strakhov, and V. I. Man’ko, Phys. Lett. A, 379, 1409 (2015).

    Article  ADS  Google Scholar 

  40. E. Glushkov, A. Glushkova, and V. I. Man’ko, J. Russ. Laser Res., 36, 448 (2015).

    Article  Google Scholar 

  41. I. Ya. Doskoch and M. A. Man’ko, J. Russ. Laser Res., 36, 503 (2015).

    Article  Google Scholar 

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

    Article  Google Scholar 

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Authors and Affiliations

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

    Margarita A. Man’ko

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  1. Margarita A. Man’ko
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Correspondence to Margarita A. Man’ko.

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Man’ko, M.A. Conditional Information and Hidden Correlations in Single-qudit States. J Russ Laser Res 38, 211–222 (2017). https://doi.org/10.1007/s10946-017-9636-6

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  • DOI: https://doi.org/10.1007/s10946-017-9636-6

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