Quantum Stein's lemma revisited, inequalities for quantum entropies, and a concavity theorem of Lieb

Details Quantum Stein's lemma revisited, inequalities for quantum entropies, and a concavity theorem of Lieb Quantum Stein's lemma revisited, inequalities for quantum entropies, and a concavity theorem of Lieb

2003-07-24

arxiv.org/abs/quant-ph/0307170v2

Physics

Quantum Physics

18 pages, no figures. Completely rewritten update of the paper: Title changed, the proofs are considerably simplified, joint c

Scientific paper

We derive the monotonicity of the quantum relative entropy by an elementary operational argument based on Stein's lemma in quantum hypothesis testing. For the latter we present an elementary and short proof that requires the law of large numbers only. Joint convexity of the quantum relative entropy is proven too, resulting in a self-contained elementary version of Tropp's approach to Lieb's concavity theorem, according to which the map tr(exp(h+log a)) is concave in a on positive operators for self-adjoint h.

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