Quantum Stein's lemma revisited, inequalities for quantum entropies, and a concavity theorem of Lieb
arXiv:quant-ph/0307170
Abstract
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.
18 pages, no figures. Completely rewritten update of the paper: Title changed, the proofs are considerably simplified, joint convexity of the relative entropy is taken into account and a self-contained, operational approach to a recent proof by Tropp of one of Lieb's concavity results for trace functions is presented. Use of the Hiai/Petz-approximation of the quantum relative entropy is avoided
References in corpus (1)
Cited by in corpus (6)
- Principles of Quantum Communication Theory: A Modern Approach
- Hypothesis testing for Gaussian states on bosonic lattices
- Hypothesis Testing on Invariant Subspaces of the Symmetric Group, Part I - Quantum Sanov's Theorem and Arbitrarily Varying Sources
- Macroscopic Thermodynamic Reversibility in Quantum Many-Body Systems
- Ancilla dimension in quantum channel discrimination
- Communication Complexity of One-Shot Remote State Preparation