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Properties of quantum entropy

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Quantum Probability and Applications II

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1136))

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Bibliography

  1. L. Accardi, Topics in quantum probability, Physics Reports, 77 (1981), 169–192.

    Article  ADS  MathSciNet  Google Scholar 

  2. L. Accardi and A Frigerio, Markovian cocyclies, Proc. Royal Irish Acad. 83A (1983), 251–263.

    MathSciNet  MATH  Google Scholar 

  3. L. Accardi and S. Olla, Donsker and Varadhan's theory for stationary processes, Preprint, Rome, 1983.

    Google Scholar 

  4. H. Araki, Relative entropy of states of a von Neumann algebra, I and II, Publ. RIMS, Kyoto Univ. 11 (1976), 809–833 and 13 (1977), 173–192.

    Article  MathSciNet  MATH  Google Scholar 

  5. O. Bratteli and D. V. Robinson, Operator algebras and quantum statistical mechanics I and II, Springer Verlag, Berlin, 1981.

    Book  MATH  Google Scholar 

  6. B. C. Carlson, The logarithmic mean, Amer. Math. Monthly, 79 (1972), 615–618.

    Article  MathSciNet  MATH  Google Scholar 

  7. I. Csiszár, Information-type measures of difference of probability distributions and indirect observations, Studia Sci. Math. Hungar. 2 (1967), 299–318.

    MathSciNet  MATH  Google Scholar 

  8. M. Donsker and S. R. S. Varadhan, Asymptotic evaluation of certain Markov process expectations for large time, Comm. Pure Appl. Math. 28 (1975), 1–47.

    Article  MathSciNet  MATH  Google Scholar 

  9. V. Ya. Golodets and G. N. Zholkevich, Markovian KMS-states (in Russian), Teoret. Mat. Fiz. 56 (1983), 80–86.

    MathSciNet  Google Scholar 

  10. F. Hiai, M. Ohya and M. Tsukuda, Sufficiency, KMS condition and relative entropy in von Neumann algebras, Pacific J. Math. 96 (1981) 99–109.

    Article  MathSciNet  MATH  Google Scholar 

  11. A. S. Holevo, Some estimates for the amount of information transmittable by a quantum communication channel (in Russian), Problemy Peredaci Informacii, 9 (1973), 3–11.

    MathSciNet  Google Scholar 

  12. H. Kosaki, Interpolation theory and the Wigner-Yanase-Dyson-Lieb conjecture, Commun. Math. Phys. 87 (1982), 315–329.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. H. Kosaki, Variational expressions of relative entropy of states on W*-algebras, Preprint, 1984.

    Google Scholar 

  14. S. Kullback and R. A. Leibler, On information and sufficiency, Ann. Math. Stat. 22 (1951), 79–86.

    Article  MathSciNet  MATH  Google Scholar 

  15. E. H. Lieb, Some convexity and subadditivity properties of entropy, Bull. Amer. Math. Soc. 81 (1975), 1–14.

    Article  MathSciNet  MATH  Google Scholar 

  16. G. Lindblad, Entropy, information and quantum measurements, Commun. Math. Phys. 33 (1973), 305–322.

    Article  ADS  MathSciNet  Google Scholar 

  17. G. Lindblad, Expectations and entropy inequalities for finite quantum systems, Commun. Math. Phys. 39 (1974), 111–119.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. G. Lindblad, Letter to the author, 1984.

    Google Scholar 

  19. J. von Neumann, Mathematische Grundlagen der Quantenmechanic, Springer Verlag, Berlin, 1932.

    Google Scholar 

  20. D. Petz, The relative entropy of states of von Neumann algebras Proc. Second Intern. Conf. on Operator Algebras, Ideals and their Appl. in Theor. Physics, Teubner-Texte zur Math. 67, 112–117, Teubner Verlag, 1984.

    MathSciNet  Google Scholar 

  21. D. Petz, Properties of the relative entropy of states of a von Neumann algebra, to appear in Acta Math. Hungar.

    Google Scholar 

  22. D. Petz, Quasi-entropies for finite quantum systems, to appear in Rep. Math. Phys.

    Google Scholar 

  23. D. Petz, Quasi-entropies for states of a von Neumann algebra, Preprint, Budapest, 1984.

    Google Scholar 

  24. D. Petz, Spectral scale of selfadjoint operators and trace inequalities, to appear in J. Math. Anal. Appl.

    Google Scholar 

  25. D. Petz, Jensen's inequality for trace reducing positive mappings, in preparation.

    Google Scholar 

  26. G. A. Raggio, Comparison of Uhlmann's transition probability with the one induced by the natural positive cone of a von Neumann algebra in standard form, Lett. Math. Phys. 6 (1982), 233–236.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. G. A. Raggio, Generalized transition probabilities and applications, Quantum Prob. and Appl. to the Quant. Theor. of Irrev. Processes (ed. by L. Accardi, A. Frigerio and V. Gorini), Lecture Notes in Math. 1055, 327–335, Springer Verlag, Berlin, 1984.

    Chapter  Google Scholar 

  28. I. E. Segal, A note on the concept of entropy, J. Math. Mech. 9 (1960), 623–629.

    MathSciNet  MATH  Google Scholar 

  29. S. Stratila, Modular theory of operator algebras, Abacus Press, Tunbridge Wells, 1981.

    MATH  Google Scholar 

  30. A. Uhlmann, Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory, Commun. Math. Phys. 54 (1977), 21–32.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  31. H. Umegaki, Conditional expectations in an operator algebra IV (entropy and information), Kodai Math. Sem. Rep. 14 (1962/, 59–85.

    Article  MathSciNet  MATH  Google Scholar 

  32. A. Wehrl, A remark on the concavity of entropy, Found. Phys. 9 (1979), 939–946.

    Article  ADS  MathSciNet  Google Scholar 

  33. A. Wehrl, General properties of entropy, Rev. Modern Phys. 50 (1978), 221–260.

    Article  ADS  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Mathematical Institute, H.A.S., P.O.Box 127, H-1364, Budapest

    Dénes Petz

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  1. Dénes Petz
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Luigi Accardi Wilhelm von Waldenfels

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© 1985 Springer-Verlag

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Petz, D. (1985). Properties of quantum entropy. In: Accardi, L., von Waldenfels, W. (eds) Quantum Probability and Applications II. Lecture Notes in Mathematics, vol 1136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074491

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  • DOI: https://doi.org/10.1007/BFb0074491

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15661-1

  • Online ISBN: 978-3-540-39570-6

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