Abstract
The entropy and the mutual entropy for states and channels are totally studied in general quantum systems described byC*-algebras. In particular, we discuss the relations among theS-entropy and the mutual entropy introduced by Ohya and the Connes-Narnhofer-Thirring entropy.
Similar content being viewed by others
References
Alfsen, E., Compact Convex Sets and Boundary Integarls, Springer-Verlag, Berlin-Heidelber-New York, 1971.
Araki, H., Relative entropy for states of von Neumann algebras, Publ. RIMS, Kyoto Univ.,11(1976), pp. 809–833.
Bratteli, O. and Robinson, D. W., Operator Algebras and Quantum Statistical Mechanics I, Springer-Verlag, New York, 1981.
Connes, A., Entropie de Kolmogorov-Sinai et mechanique statistique quantique, C.R. Acad. Sci. Paris t. 301 I, 1 (1985).
Connes, A., H. Narnhofer and W. Thirring, Dynamical entropy ofC*-algebras and von Neumann algebras, Commun. Math. Phys.,112(1987), pp. 691–719.
Connes, A. and Størmer, E., Entropy of automorphisms of II1-von Neumann algebras, Acta Math.,134(1975), 289.
Manuceau, J., Naudts, J. and Verbeure, A., Entropy and normal states, Commun. Math. Phys.27(1973), pp. 327–338.
Muraki, N., Remarks on continuity of entropy of states onC*-dynamical systems, J. Math. Phys.,32(1991), pp. 1796–1798.
Narnhofer, H. and Thirring, W., From relative entropy to entropy, Fizika,17(1985), 259.
von Neuamnn, J., Mathematische Grundlagen der Quantenmechanik, Springer, Berlin, 1932.
Ohya, M., On compound states and mutual information in quantum information theory, IEEE Transactions on Information Theory,29(1983), pp. 770–774.
Ohya, M., Entropy transmission inC*-dynamical sysytems, J. Math. Anal. Appl.,100(1984), pp. 222–235.
Ohya, M., State change and entropies in quantum dynamical systems, Springer Lecture Notes in Mathematics, No. 1136 (1985), pp. 397–408.
Ohya, M., Some aspects of quantum information theory and its applications to irreversible processes, Rep. Math. Phys.,27(1989), pp. 19–47.
Ohya, M., Information dynamics and its applications to optical communication processes, Springer Lecture Notes in Physics, No. 378 (1991), pp. 81–92.
Ohya, M. and Matsuoka, T., Continuity of entropy and mutual entropy inC*-dynamical systems, J. Math. Phys.,27(1986), pp. 2076–2078.
Ohya, M. and Petz, D., Quantum Entropy and its Use, to be published by Springer-Verlag.
Petz, D., Properties of quantum entropy, Quantum Probability and Applications, Lecture Notes in Math., No. 1136 (1985), pp. 428–441, Springer.
Uhlmann, A., Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in interpolation theory, Commun. Math. Phys.,54(1977), pp. 21–32.
Umegaki, H., Conditional expectations in operator algebras IV, Kodai Math. J.14(1962), pp. 59–85.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Muraki, N., Ohya, M. & Petz, D. Entropies of general quantum states. Open Syst Inf Dyn 1, 43–56 (1992). https://doi.org/10.1007/BF02228935
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02228935