An ergodic theorem for the quantum relative entropy

Communications in Mathematical Physics

Volumn 247, Issue 3, 2004, Pages 697-712

  Bjelaković, Igor ^a   Siegmund Schultze, Rainer ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2942733388     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-004-1054-2     Document Type: Article

References (8)

1. Bjelaković, I., Krüger, T., Siegmund-Schultze, Ra., Szkoła, A.: The Shannon-McMillan Theorem for Ergodic Quantum Lattice Systems. arXiv.org, math.DS/0207121. Invent. Math. 155, 203-222 (2004)
2. Bratteli, O., Robinson, D.W.: Operator Algebras and Quantum Statistical Mechanics I. New York: Springer, 1979
3. Hiai, F., Petz, D.: The Proper Formula for Relative Entropy and its Asymptotics in Quantum Probability. Commun. Math. Phys. 143, 99-114 (1991)
4. Ogawa, T., Nagaoka, H.: Strong Converse and Stein's Lemma in Quantum Hypothesis Testing. IEEE Trans. Inform. Theo. 46(7), 2428-2433 (2000)
5. Ohya, M., Petz, D.: Quantum Entropy and its Use. Berlin: Springer, 1993
6. Ornstein, D., Weiss, B.: The Shannon-McMillan-Breiman Theorem for a Class of Amenable Groups. Israel J. Math. 44(1), 53-60 (1983)
7. Ruelle, D.: Statistical Mechanics. New York: W.A. Benjamin, 1969
8. Shields, P.C.: Two divergence-rate counterexamples. J. Theor. Prob. 6, 521-545 (1993)