An Ergodic Theorem for the Quantum Relative Entropy
Quantum Physics
2009-11-10 v1 Mathematical Physics
math.MP
Probability
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
Cite
@article{arxiv.quant-ph/0306094,
title = {An Ergodic Theorem for the Quantum Relative Entropy},
author = {Igor Bjelakovic and Rainer Siegmund-Schultze},
journal= {arXiv preprint arXiv:quant-ph/0306094},
year = {2009}
}
Comments
19 pages, no figures