Chain Rule for the Quantum Relative Entropy

The chain rule for the classical relative entropy ensures that the relative entropy between probability distributions on multipartite systems can be decomposed into a sum of relative entropies of suitably chosen conditional distributions on the individual systems. Here, we prove a chain rule inequal...

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Bibliographic Details
Published inPhysical review letters Vol. 124; no. 10; p. 100501
Main Authors Fang, Kun, Fawzi, Omar, Renner, Renato, Sutter, David
Format Journal Article
LanguageEnglish
Published United States 13.03.2020
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Summary:The chain rule for the classical relative entropy ensures that the relative entropy between probability distributions on multipartite systems can be decomposed into a sum of relative entropies of suitably chosen conditional distributions on the individual systems. Here, we prove a chain rule inequality for the quantum relative entropy. The new chain rule allows us to solve an open problem in the context of asymptotic quantum channel discrimination: surprisingly, adaptive protocols cannot improve the error rate for asymmetric channel discrimination compared to nonadaptive strategies.
ISSN:1079-7114
DOI:10.1103/PhysRevLett.124.100501