From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture

DOI10.1016/j.aim.2020.107053zbMath1435.15005arXiv1811.01205OpenAlexW3005935076WikidataQ122917537 ScholiaQ122917537MaRDI QIDQ2308308

Haonan Zhang

Publication date: 2 April 2020

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.01205

zbMATH Keywords

quantum relative entropydata processing inequalityjoint convexity/concavity

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Miscellaneous inequalities involving matrices (15A45) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Algebraic systems of matrices (15A30) Measures of information, entropy (94A17) Quantum information, communication, networks (quantum-theoretic aspects) (81P45)

Related Items (16)

Convexity of a certain operator trace functional ⋮ Multivariate trace inequalities, p-fidelity, and universal recovery beyond tracial settings ⋮ Geometric conditions for saturating the data processing inequality ⋮ Generalizing Lieb's concavity theorem via operator interpolation ⋮ The strong converse exponent of discriminating infinite-dimensional quantum states ⋮ Monotonic multi-state quantum f-divergences ⋮ Optimal Self-Concordant Barriers for Quantum Relative Entropies ⋮ Equality cases in monotonicity of quasi-entropies, Lieb’s concavity and Ando’s convexity ⋮ Interpolation between modified logarithmic Sobolev and Poincaré inequalities for quantum Markovian dynamics ⋮ Lieb type convexity for positive operator monotone decreasing functions ⋮ Some convexity and monotonicity results of trace functionals ⋮ Equality conditions of data processing inequality for α-z Rényi relative entropies ⋮ Variational representations related to quantum Rényi relative entropies ⋮ Unnamed Item ⋮ Monotonicity versions of Epstein's Concavity Theorem and related inequalities ⋮ Closest separable state when measured by a quasi-relative entropy

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