An Ergodic Theorem for the Quantum Relative Entropy

Details An Ergodic Theorem for the Quantum Relative Entropy An Ergodic Theorem for the Quantum Relative Entropy

2003-06-13

arxiv.org/abs/quant-ph/0306094v1

Physics

Quantum Physics

19 pages, no figures

Scientific paper

10.1007/s00220-004-1054-2

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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