Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Korean Journal of Mathematics

INEQUALITIES FOR QUANTUM f-DIVERGENCE OF CONVEX FUNCTIONS AND MATRICES

Sever S Dragomir

Published Sep 30, 2018• 0 citations
Publisher

Abstract

Some inequalities for quantum $f$-divergence of matrices are obtained. It is shown that for normalised convex functions it is nonnegative. Some upper bounds for quantum $f$-divergence in terms of variational and $\chi ^{2}$-distance are provided. Applications for some classes of divergence measures such as Umegaki and Tsallis relative entropies are also given.

DOI
10.11568/kjm.2018.26.3.349

Related papers

Inequalities for Quantum f-Divergence of Trace Class Operators in Hilbert Spaces

Dragomir, Silvestru Sever

Some inequalities for quantum f-divergence of trace class operators in Hilbert spaces are obtained. It is shown that for normalised convex functions it is nonnegative. Some upper bounds for quantum f-divergence in terms of variational and chi-distance are provided. Applications for some classes of divergence measures such as Umegaki and Tsallis relative entropies are also given.

arXiv:1509.04362•Sep 15, 2015•0 citations

A New Quantum f-Divergence for Trace Class Operators in Hilbert Spaces

Sever S Dragomir

A new quantum f-divergence for trace class operators in Hilbert Spaces is introduced. It is shown that for normalised convex functions it is nonnegative. Some upper bounds are provided. Applications for some classes of convex functions of interest are also given.

Entropy•Nov 6, 2014•3 citations

Some applications of the Hermit-Hadamard inequality for log-convex functions in quantum divergence

Fatemeh Hassanzad, Hossien Mehri-Dehnavi, Hamzeh Agahi

One of the beautiful and very simple inequalities for a convex function is the Hermit-Hadamard inequality [S. Mehmood, et. al. Math. Methods Appl. Sci., 44 (2021) 3746], [S. Dragomir, et. al., Math. Methods Appl. Sci., in press]. The concept of log-convexity is a stronger property of convexity. Recently, the refined Hermit-Hadamard’s inequalities for log-convex functions were introduced by researchers [C. P. Niculescu, Nonlinear Anal. Theor., 75 (2012) 662]. In this paper, by the Hermit-Hadamard inequality, we introduce two parametric Tsallis quantum relative entropy, two parametric Tsallis-Lin quantum relative entropy and two parametric quantum Jensen-Shannon divergence in quantum information theory. Then some properties of quantum Tsallis-Jensen-Shannon divergence for two density matrices are investigated by this inequality. \newline \textbf{Keywords:} \textit{ Hermit-Hadamard’s inequality; log-convexity; Density matrices; Quantum relative entropy; Tsallis quantum relative entropy; quantum Jensen-Shannon divergence divergence.

•Jul 23, 2021•0 citations

Quantum Tsallis-Jensen-Shannon divergence and its bounds

Fatemeh Hassanzad, Hossein Mehri‐Dehnavi, Hamzeh Agahi

In this paper, we first introduce some properties of quantum Tsallis-Jensen-Shannon divergence for two density matrices. Then one of the beautiful and very simple applications of Hermit-Hadamard’s inequality [S. Dragomir, et. al. Math. Methods Appl. Sci., 1–15 (2020)] for log-convexity in the concepts of quantum entropies and quantum Tsallis-Jensen-Shannon is given.

•Jan 30, 2024•0 citations

A Collection of Pinsker-type Inequalities for Quantum Divergences

Kläre Wienecke, Gereon Koßmann, René Schwonnek

Pinsker's inequality sets a lower bound on the Umegaki divergence of two quantum states in terms of their trace distance. In this work, we formulate corresponding estimates for a variety of quantum and classical divergences including $f$-divergences like Hellinger and $χ^2$-divergences as well as Rényi divergences and special cases thereof like the Umegaki divergence, collision divergence, max divergence. We further provide a strategy on how to adapt these bounds to smoothed divergences.

quant-pharXiv:2601.10395•IEEE International Symposium on Information Theory (ISIT)•Jan 16, 2026•1 citation

Some applications of the Hermite–Hadamard inequality for log‐convex functions in quantum divergences

Fatemeh Hassanzad, Hossein Mehri‐Dehnavi, Hamzeh Agahi

One of the beautiful and very simple inequalities for a convex function is the Hermite–Hadamard inequality. The concept of ‐convexity is a strong variant of convexity. In this paper, by the Hermite–Hadamard inequality, we introduce two‐parametric Tsallis quantum relative entropy, two‐parametric Tsallis–Lin quantum relative entropy, and two‐parametric quantum Jensen–Shannon divergence in quantum information theory. Then some properties of quantum Tsallis–Jensen–Shannon divergence for two density matrices are investigated by this inequality.

Mathematical Methods in the Applied Sciences•Feb 24, 2022•0 citations
Some inequalities for quantum fff-divergence of matrices are obtained. It is shown that for normalised convex functions it is nonnegative. Some upper bounds for quantum fff-divergence in terms of variational and χ2\chi ^{2}χ2-distance are provided. Applications for some classes of divergence measures such as Umegaki and Tsallis relative entropies are also given.
One of the beautiful and very simple inequalities for a convex function is the Hermit-Hadamard inequality [S. Mehmood, et. al. Math. Methods Appl. Sci., 44 (2021) 3746], [S. Dragomir, et. al., Math. Methods Appl. Sci., in press]. The concept of log-convexity is a stronger property of convexity. Recently, the refined Hermit-Hadamard’s inequalities for log-convex functions were introduced by researchers [C. P. Niculescu, Nonlinear Anal. Theor., 75 (2012) 662]. In this paper, by the Hermit-Hadamard inequality, we introduce two parametric Tsallis quantum relative entropy, two parametric Tsallis-Lin quantum relative entropy and two parametric quantum Jensen-Shannon divergence in quantum information theory. Then some properties of quantum Tsallis-Jensen-Shannon divergence for two density matrices are investigated by this inequality. \newline \textbf{Keywords:} \textit{ Hermit-Hadamard’s inequality; log-convexity; Density matrices; Quantum relative entropy; Tsallis quantum relative entropy; quantum Jensen-Shannon divergence divergence.
Pinsker's inequality sets a lower bound on the Umegaki divergence of two quantum states in terms of their trace distance. In this work, we formulate corresponding estimates for a variety of quantum and classical divergences including fff-divergences like Hellinger and χ2χ^2χ2-divergences as well as Rényi divergences and special cases thereof like the Umegaki divergence, collision divergence, max divergence. We further provide a strategy on how to adapt these bounds to smoothed divergences.
One of the beautiful and very simple inequalities for a convex function is the Hermite–Hadamard inequality. The concept of ‐convexity is a strong variant of convexity. In this paper, by the Hermite–Hadamard inequality, we introduce two‐parametric Tsallis quantum relative entropy, two‐parametric Tsallis–Lin quantum relative entropy, and two‐parametric quantum Jensen–Shannon divergence in quantum information theory. Then some properties of quantum Tsallis–Jensen–Shannon divergence for two density matrices are investigated by this inequality.