Abstract
The rigorous formulation of the quantum mutual entropy is reviewed. The capacities for various channels, such as quantum channel, classical-quantum channel and classical-quantum-classical channel are discussed exhaustively and some misuses of these capacities are indicated.
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Bibliography
L. Accardi, M. Ohya, and H. Suyari, Open Sys. Information Dyn. 2, 337 (1994).
S. Akashi, J. Math. Anal. Appi. 153, 250 (1990).
R. Alicki, Open Sys. Information Dyn. 4, 53 (1997).
H. Araki, Pubi. RIMS Kyoto Univ. 11, 809 (1976).
V. P. Belavkin, Proc. of VIII-th Conference on Codzng Theory and Information Transrnis-sion, Moscow-Kuibishev, 1982, p. 15.
V.P. Belavkin and P. L. Stratonovich, Radio Eng. Electron. Phys. 18, 1839 (1973).
P. Billingsley, Ergodic Theory and Information, Wiley, NY.,1965.
1. M. Gelfand and A. M. Yaglom, Amer. Math. Soc. Transl. 12, 199 (1959).
A. S. Holevo, Problemy Peredachi lnformacii 9, 3 (1973), in Russian.
R.S. Ingarden, Rep. Math. Phys. 10, 43(1976).
R. S. Ingarden, A. Kossakowski and M. Ohya, Information Dynamics ond Open Systems, Kluwer Academic Publisher, 1997.
K. Jnoue, M. Ohya, and H. Suyari, Physica D 120, 117 (1998).
AN. Kolmogorov, Amer. Math. Soc. Translation, Ser.2 33, 291 (1963).
S. Kuliback and R. Leibler, Ann. Math. Stat. 22, 79 (1951).
L.B. Levitin, Springer Lect. Note in Phys. 378, 101 (1991).
C.Lindblad, Commun. Math. Phys., 33, 111 (1973).
T. Matsuoka and M. Ohya, Rep. Math. Phys. 36, 365 (1995).
N. Muraki, M. Ohya, and D. Petz, Open Sys. Information Dyn. 1, 43 (1992).
N. Muraki and M. Ohya, Lett. Math. Phys. 36, 327 (1996).
J. von Neumann, Die Mathe,natischen Grundlagen der Quantenrneehanik, Springer-Berlin, 1932.
M. Ohya, J. Math. Anal. Appl. 84, 318 (1981).
M. Ohya, IEEE Trans. Information Theory, 29, 770 (1983).
M. Ohya, L. Nuovo Cimento 38, 402 (1983).
M. Ohya, Rep. Math. Phys. 27, 19 (1989).
M. Ohya, Quantum Probability and Related Topics 6, World Scientific, Singapore, 1991.
M. Ohya, Quantum Communications and Measurement, p. 309, 1995.
M. Ohya, Open Sys. Information Dyn. 4, 141 (1997).
M. Ohya, mt. J. Theor. Phys. 37, 495 (1998).
M. Ohya and D. Petz, Quantum Entropy and Its Use, Springer, 1993.
M. Ohya, D. Petz, and N. Watanabe, Probability and Mathematical Statistics, 17, 179 (1997).
M. Ohya, D. Petz, and N. Watanabe, mt. J. Theor. Phys. 38, 507 (1998).
M. Ohya and N. Watanabe, Physica D 120, 206 (1998).
C. E. Shannon, Bell System Tech. J. 27, 379 (1948).
R. Schatten, Norm Ideals of Completely Continuous Operators, Springer-Verlag, 1970.
A. Uhlmann, Commun. Math. Phys. 54, 21 (1977).
H. Umegaki, Kodai Math. Sem. Rep. 14, 59 (1962).
H.P. Yuen and M. Ozawa, Phys. Rev. Lett. 70, 363 (1993).
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Ohya, M. Fundamentals of Quantum Mutual Entropy and Capacity. Open Systems & Information Dynamics 6, 69–78 (1999). https://doi.org/10.1023/A:1009676318267
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DOI: https://doi.org/10.1023/A:1009676318267