Abstract
Information dynamics was proposed in [1] and it is a synthesis of the dynamics of state change and the theory of complexity. Information dynamics is now developing for uses in several different topics such as quantum physics, fractal theory, quantum information and genetics. Here we discuss entropic complexities in quantum systems and some applications to quantum communication process and Fractal theory.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ohya, M.: “Information dynamics and its application to optical communication processes”, Lecture Notes in Physics 378, Springer, 1991, pp. 81–92.
Ohya, M.: “Entropy change in linear response dynamics”, Nuovo Cimento, 91B, 1986, pp. 25–30.
Ohya, M.: “Some aspects of quantum information theory and the applications to irreversible processes”, Rep. M.th. Phys., 27, 1989, pp. 19–47.
Accardi, L. and Ohya, M.: “Compound channels, transition expectations and liftings”, to appear in J. Multivariate Analysis.
Ohya, M: “Note on quantum probability”, L. Nuovo Cimento, 38, 1983, pp. 402–406.
Accardi L.: “Noncommutative Markov chains” In: international School of Mathematical Physics, Camerino, 1974, 268–295.
Accardi L., Ohya M. and Suyari H.: “Computation of mutual entropy in quantum Markov chains”, preprint in CENTRO MATEMATICO V.VOLTERRA.
Ohya, M: “On compound state and mutual information in quantum information theory”, IEEE Trans. Information Theory, 1983, 29, pp. 770–777.
Choquet G.: Lecture Analysis I, II, III, Benjamin, New York, 1969.
Connes, A. Narnhofer, H. and Thirring, W.: “Dynamical entropy of C*- algebras and von Neumann algebras”, Commun Math. Phys. 112, 1987, pp. 691–719.
Muraki, N., Ohya, M. and Petz, D.: “Entropies of general quantum systems”, Open Systems and Information Dynamics, 1 (No.1), 1992, pp. 43–56.
Ohya M. and Petz D.: “Quantum Entropy and its Use”, Springer-Verlag 1993.
Araki, H.: “Relative entropy for states of von Neumann algebras Publ. RIMS Kyoto Univ. 11, 1976, pp. 809–833.
Uhlmann, A.: “Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory”, Commun Math. Phys. 54, 1977, pp. 21–32.
Ohya, M.: in preparation.
Ohya, M. and Watanabe, N.: “A mathematical study of information transmission in quantum communication processes”, in this volume.
Accardi L., Ohya M. and Suyari H.: “Mutual entropy in quantum Markov chains”, in this volume.
Muraki, N. and Ohya, M. preprint.
Kolmogorov, A.N.: “Theory of transmission of information”, Amer. Math. Soc. Translation, Ser.2, 33, 1963, pp. 291-.
Ohya, M.: “Fractal dimensions of states”, Quantum Probability and Related Topics VI, 1991, pp. 359–369.
Akashi, S.: “A relation between Kolmogorov-Prokhorov’s condition and Ohya’s fractal dimensions”, IEEE Transaction on Inf. Theory., 38, 1992, pp. 1567–1570.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media New York
About this chapter
Cite this chapter
Ohya, M. (1995). State Change, Complexity and Fractal in Quantum Systems. In: Belavkin, V.P., Hirota, O., Hudson, R.L. (eds) Quantum Communications and Measurement. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1391-3_29
Download citation
DOI: https://doi.org/10.1007/978-1-4899-1391-3_29
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-1393-7
Online ISBN: 978-1-4899-1391-3
eBook Packages: Springer Book Archive