From quasi-entropy to various quantum information quantities

DOI10.2977/PRIMS/79zbMath1256.81024MaRDI QIDQ713084

Fumio Hiai, Dénes Petz

Publication date: 26 October 2012

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

zbMATH Keywords

monotone metricquasi-entropygeneralized covariance\(f\)-divergence\(\chi^2\)-divergence

Mathematics Subject Classification ID

Entropy in general topology (54C70) Measures of information, entropy (94A17) Quantum information, communication, networks (quantum-theoretic aspects) (81P45)

Related Items (18)

Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance ⋮ A new quantum \(f\)-divergence for trace class operators in Hilbert spaces ⋮ Maps on positive definite operators preserving the quantum \(\chi_\alpha ^2\)-divergence ⋮ Equality cases in monotonicity of quasi-entropies, Lieb’s concavity and Ando’s convexity ⋮ Characterizing Schwarz maps by tracial inequalities ⋮ Some convexity and monotonicity results of trace functionals ⋮ Convexity of quasi-entropy type functions: Lieb's and Ando's convexity theorems revisited ⋮ Completely positive mappings and mean matrices ⋮ Contraction coefficients for noisy quantum channels ⋮ Optimized quantumf-divergences and data processing ⋮ Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Quantum Aitchison geometry ⋮ Monotonicity versions of Epstein's Concavity Theorem and related inequalities ⋮ Monotonicity of skew information and its applications in quantum resource theory ⋮ Stability of logarithmic Sobolev inequalities under a noncommutative change of measure ⋮ INEQUALITIES FOR QUANTUM f-DIVERGENCE OF CONVEX FUNCTIONS AND MATRICES

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