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Some applications of the Hermit-Hadamard inequality for log-convex functions in quantum divergence
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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.
Title: Some applications of the Hermit-Hadamard inequality for log-convex functions in quantum divergence
Description:
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.
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