From joint convexity of quantum relative entropy to a concavity theorem of Lieb

Abstract

This note provides a succinct proof of a 1973 theorem of Lieb that establishes the concavity of a certain trace function. The development relies on a deep result from quantum information theory, the joint convexity of quantum relative entropy, as well as a recent argument due to Carlen and Lieb.

3 pages

Cited by in corpus (10)

• User-friendly tail bounds for sums of random matrices
• Semidefinite approximations of the matrix logarithm
• Strong converse exponent for classical-quantum channel coding
• Variational Principle of Bogoliubov and Generalized Mean Fields in Many-Particle Interacting Systems
• On the joint convexity of the Bregman divergence of matrices
• Approximate quantum Markov chains
• Multivariate Trace Inequalities, p-Fidelity, and Universal Recovery Beyond Tracial Settings
• Variational representations related to Tsallis relative entropy
• Geometric relative entropies and barycentric Rényi divergences
• Adaptive Online Learning of Quantum States