A quantum version of Sanov's theorem

Communications in Mathematical Physics

Volumn 260, Issue 3, 2005, Pages 659-671

  Bjelaković, Igor ^a   Deuschel, Jean Dominique ^a   Krüger, Tyll ^a,b   Seiler, Ruedi ^a   Siegmund Schultze, Rainer ^a,c   Szkoła, Arleta ^a,d  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^b BIELEFELD UNIVERSITY   (Germany)

^c ILMENAU UNIVERSITY OF TECHNOLOGY   (Germany)

^d MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 27244438404     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-005-1426-2     Document Type: Article

References (17)

1. Bjelaković, I., Krüger, T., Siegmund-Schultze, Ra., Szkola, A.: The Shannon-McMillan theorem for ergodic quantum lattice systems. Invent. Math. 155(1), 203-222 (2004)
2. Bjelaković, I., Krüger, T., Siegmund-Schultze, Ra., Szkola, A.: Chained typical subspaces-A quantum version of Breiman's theorem, http://arxiv.org/list/quant-ph/0301177, 2003
3. Bjelaković, I., Szkola, A.: The data compression theorem for ergodic quantum information sources. Quant. Inform. Proc. 4(1), 49-63 (2005)
4. Bjelaković, I., Deuschel, J.-D., Krüger, T., Seiler, R., Siegmund-Schultze, Ra., Szkola, A.: A Sanov type theorem for ergodic probability measures and its quantum extension. In preparation
5. Bjelaković, I., Siegmund-Schultze, Ra.: An Ergodic Theorem for the Quantum Relative Entropy. Commun. Math. Phys. 247, 697-712 (2004)
6. Bjelaković, I., Siegmund-Schultze, Ra.: A New Proof of the Monotonicity of Quantum Relative Entropy for Finite Dimensional Systems, http:arxiv.org/list/quant-ph/0307170, 2003
7. Cover, T.M., Thomas, J.A.: Elements of Information Theory. New York: John Wiley and Sons, 1991
8. Deuschel, J.-D., Stroock, D.W.: Large Deviations. Boston: Acad. Press, 2001
9. Gautschi, W.: Norm estimations for inverses of Vandermonde matrices. Numerische Mathematik, 23, 337-347 (1975)
10. Hiai, F., Petz, D.: The Proper Formula for Relative Entropy and its Asymptotics in Quantum Probability. Commun. Math. Phys. 143, 99-114 (1991)
11. Jozsa, R., Schumacher, B. : A New Proof of the Quantum Noiseless Coding Theorem. J. Mod. Optics 41(12). 2343-2349 (1994)
12. Kaltchenko, A., Yang, E.H.: Universal Compression of Ergodic Quantum Sources. Quant. Inf. and Comput. 3, 359-375 (2003)
13. Ogawa, T., Nagaoka, H.: Strong Converse and Stein's Lemma in Quantum Hypothesis Testing. IEEE Trans. Inf. Th. 46(7), 2428-2433 (2000)
14. Ohya, M., Petz, D.: Quantum entropy and its use. Berlin-Heidelberg-New York: Springer-Verlag, 1993
15. Sanov, I.N.: On the probability of large deviations of random variables. Mat. Sbomik 42, 11-44 (1957)
16. Shields, P.C.: Two divergence-rate counterexamples. J. Theor. Prob. 6, 521-545 (1993)
17. Takesaki, M.: Theory of operator algebras I. Berlin-Heidelberg-New York: Springer-Verlag, 1979