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arXiv quant-ph/03060942003-06-13quant-phmath-phmath.MPmath.PR

An Ergodic Theorem for the Quantum Relative Entropy

Igor Bjelakovic, Rainer Siegmund-Schultze

备注：: 19 pages, no figures
DOI：: 10.1007/s00220-004-1054-2

英文摘要：

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.

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