Matrix trace inequalities related to the Tsallis relative entropies of real order

DOI10.1016/j.jmaa.2020.124877zbMath1459.81013OpenAlexW3118927517MaRDI QIDQ1998602

Yuki Seo, Masatoshi Fujii

Publication date: 7 March 2021

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2020.124877

zbMATH Keywords

positive definite matrixTsallis relative entropymatrix geometric meanrelative operator entropy

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Positive matrices and their generalizations; cones of matrices (15B48) Quantum state spaces, operational and probabilistic concepts (81P16) Quantum entropies (81P17)

Related Items (3)

The quantum ♮α-Rényi divergence of real order ⋮ Relative Operator Entropy ⋮ Reverse of Fujii-Seo type log-majorization and its application to the Tsallis relative entropies

Cites Work

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• A Mathematical Theory of Communication
• Majorization, doubly stochastic matrices, and comparison of eigenvalues
• The Golden-Thompson trace inequality is complemented
• Means of positive linear operators
• Matrix trace inequalities on Tsallis relative entropy of negative order
• Generalized Shannon inequalities based on Tsallis relative operator entropy
• Inequalities for quantum relative entropy
• Monotonic decrease of the quantum nonadditive divergence by projective measurements
• Reverse inequalities involving two relative operator entropies and two relative entropies
• Fundamental properties of Tsallis relative entropy
• A note on the entropy for operator algebras
• Convexity inequalities for estimating free energy and relative entropy
• An extension of Specht's theorem via Kantorovich inequality and related results
• Conditional expectation in an operator algebra. IV. Entropy and information
• $A \geq B \geq 0$ Assures $(B^r A^p B^r)^{1/q} \geq B^{(p+2r)/q$ for $r \geq 0$, $p \geq 0$, $q \geq 1$ with $(1 + 2r)q \geq p + 2r$
• On Information and Sufficiency
• Inequalities: theory of majorization and its applications

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