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Communications in Mathematical Physics

, Volume 247, Issue 3, pp 697–712 | Cite as

An Ergodic Theorem for the Quantum Relative Entropy

  • Igor Bjelaković
  • Rainer Siegmund-SchultzeEmail author
Article

Abstract:

We prove the ergodic version of the quantum Stein’s lemma which was conjectured by Hiai and Petz. The result provides an operational and statistical interpretation of the quantum relative entropy as a statistical measure of distinguishability, and contains as a special case the quantum version of the Shannon-McMillan theorem for ergodic states. A version of the quantum relative Asymptotic Equipartition Property (AEP) is given.

Keywords

Entropy Stein Statistical Measure Relative Entropy Ergodic Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Technische Universität BerlinFakultät II - Mathematik und Naturwissenschaften, Institut für Mathematik MA 7-2BerlinGermany

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