Abstract
We review some notions for general quantum entropies. The entropy of the compound systems is discussed and a numerical computation of the quantum dynamical systems is carried for the noisy optical channel.
Similar content being viewed by others
References
Accardi, L., Ohya, M.: Compound channels, transition expectation and liftings. Appl. Math. Optim. 39, 33–59 (1999)
Accardi, L., Ohya, M., Watanabe, N.: Dynamical entropy through quantum Markov chain. Open Syst. Inf. Dyn. 4, 71–87 (1997)
Accardi, L., Ohya, M., Watanabe, N.: Note on quantum dynamical entropies. Rep. Math. Phys. 38, 457–469 (1996)
Alicki, R., Fannes, M.: Defining quantum dynamical entropy. Lett. Math. Phys. 32, 75–82 (1994)
Araki, H.: Relative entropy for states of von Neumann algebras. Publ. RIMS Kyoto Univ. 11, 809–833 (1976)
Benatti, F.: Deterministic Chaos in Infinite Quantum Systems. Springer, Berlin (1993)
Choda, M.: Entropy for extensions of Bernoulli shifts. Ergod. Theory Dyn. Syst. 16(6), 1197–1206 (1996)
Connes, A., Narnhoffer, H., Thirring, W.: Dynamical entropy of C*algebras and von Neumann algebras. Commun. Math. Phys. 112, 691–719 (1987)
Connes, A., Störmer, E.: Entropy for automorphisms of von Neumann algebras. Acta Math. 134, 289–306 (1975)
Emch, G.G.: Positivity of the K-entropy on non-abelian K-flows. Z. Wahrscheinlichkeitstheory verw. Gebiete 29, 241 (1974)
Fichtner, K.H., Freudenberg, W., Liebscher, V.: Beam splittings and time evolutions of Boson systems, Fakultat fur Mathematik und Informatik, Math/Inf/96/39, Jena, 105 (1996)
Hudetz, T.: Topological entropy for appropriately approximated C*-algebras. J. Math. Phys. 35(8), 4303–4333 (1994)
Ingarden, R.S., Kossakowski, A., Ohya, M.: Information Dynamics and Open Systems. Kluwer, Dordrecht (1997)
Jamiołkowski, A.: Linear transformations which preserve trace and positive semidefiniteness of operators. Rep. Math. Phys. 3, 275–278 (1972)
Khrennikov, A.: Contextual Approach to Quantum Formalism. Series of fundamental theories of physics. Springer, Berlin (2009)
Khrennikov, A.: A classical field theory comeback? The classical field viewpoint on triparticle entanglement. Phys. Scripta, T143, Article Number: 014013 (2011). doi:10.1088/0031-8949/2011/T143/014013
Kolmogorov, A.N.: Theory of transmission of information. Am. Math. Soc. Transl. Ser. 2 33, 291 (1963)
von Neumann, J.: Die Mathematischen Grundlagen der Quantenmechanik. Springer, Berlin (1932)
Kossakowski, A., Ohya, M., Watanabe, N.: Quantum dynamical entropy for completely positive map. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 2(2), 267–282 (1999)
Ohya, M.: Quantum ergodic channels in operator algebras. J. Math. Anal. Appl. 84, 318–328 (1981)
Ohya, M.: On compound state and mutual information in quantum information theory. IEEE Trans. Inf. Theory 29, 770–774 (1983)
Ohya, M.: Note on quantum probability. L. Nuovo Cimento 38, 402–404 (1983)
Ohya, M.: Some aspects of quantum information theory and their applications to irreversible processes. Rep. Math. Phys. 27, 19–47 (1989)
Ohya, M.: State change, complexity and fractal in quantum systems. Quantum Commun. Meas. 2, 309–320 (1995)
Ohya, M., Petz, D.: Quantum Entropy and Its Use. Springer, Berlin (1993)
Ohya, M., Watanabe, N.: Foundation of Quantum Communication Theory (in Japanese). Makino Publishing Company, Tokyo (1998)
Ohya, M., Watanabe, N.: Construction and analysis of a mathematical model in quantum communication processes. Electron. Commun. Jpn. Part 1 68(2), 29–34 (1985)
Ohya, M., Volovich, I.: Mathematical Foundations of Quantum Information and Computation and Its Applications to Nano- and Bio-systems. Springer, Dordrecht (2011)
Park, Y.M.: Dynamical entropy of generalized quantum Markov chains. Lett. Math. Phys. 32, 63–74 (1994)
Schatten, R.: Norm Ideals of Completely Continuous Operators. Springer, Berlin (1970)
Tuyls, P.: Comparing quantum dynamical entropies. Banach Centre Publ. 43, 411–420 (1998)
Umegaki, H.: Conditional expectations in an operator algebra IV (entropy and information). Kodai Math. Sem. Rep. 14, 59–85 (1962)
Uhlmann, A.: Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in interpolation theory. Commun. Math. Phys. 54, 21–32 (1977)
Voiculescu, D.: Dynamical approximation entropies and topological entropy in operator algebras. Commun. Math. Phys. 170, 249–281 (1995)
Watanabe, N.: Note on entropies of quantum dynamical systems. Found. Phys. 41, 549–563 (2011). doi:10.1007/s10701-010-9455-x
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Watanabe, N. On Entropy of Quantum Compound Systems. Found Phys 45, 1311–1329 (2015). https://doi.org/10.1007/s10701-015-9925-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10701-015-9925-2