相关论文: A Matrix Convexity Approach to Some Celebrated Qua…

Some of the important inequalities associated with quantum entropy are immediate algebraic consequences of the Hansen-Pedersen-Jensen inequality. A general argument is given in terms of the matrix perspective of an operator convex function.…

We investigate the quantum Jensen divergences from the viewpoint of joint convexity. It turns out that the set of the functions which generate jointly convex quantum Jensen divergences on positive matrices coincides with the Matrix Entropy…

This paper presents self-contained proofs of the strong subadditivity inequality for quantum entropy and some related inequalities for the quantum relative entropy, most notably its convexity and its monotonicity under stochastic maps.…

A considerable amount of literature in the theory of inequality is devoted to the study of Jensen's and Young's inequality. This article presents a number of new inequalities involving the log-convex functions and the geometrically convex…

This short but self-contained survey presents a number of elegant matrix/operator inequalities for general convex or concave functions, obtained with a unitary orbit technique. Jensen, sub or super-additivity type inequalities are…

In this paper we point out a converse result of the celebrated Jensen inequality for differentiable convex mappings of several variables and apply it to counterpart well-known analytic inequalities. Applications to Shannon's and Renyi's…

In this article, we employ a standard convex argument to obtain new and refined inequalities related to the matrix mean of two accretive matrices, the numerical radius and the Tsallis relative operator entropy.

We study the fundamental properties of the quantum f-relative entropy, where f(.) is an operator convex function. We give the equality conditions under monotonicity and joint convexity, and these conditions are more general than, since they…

We introduce a generalization of relative entropy derived from the Wigner-Yanase-Dyson entropy and give a simple, self-contained proof that it is convex. Moreover, special cases yield the joint convexity of relative entropy, and for the map…

Many trace inequalities can be expressed either as concavity/convexity theorems or as monotonicity theorems. A classic example is the joint convexity of the quantum relative entropy which is equivalent to the Data Processing Inequality. The…

Some rearrangement inequalities for symmetric norms on matrices are given as well as related results for operator convex functions.

A short and elementary proof of the joint convexity of relative entropy is presented, using nothing beyond linear algebra. The key ingredients are an easily verified integral representation and the strategy used to prove the Cauchy-Schwarz…

Some mathematical inequalities among various weighted means are studied. Inequalities on weighted logarithmic mean are given. Besides, the gap in Jensen's inequality is studied as a convex function approach. Consequently, some non-trivial…

An inequality in quantum mechanics, which does not appear to be well known, is derived by elementary means and shown to be quite useful. The inequality applies to 'all' operators and 'all' pairs of quantum states, including mixed states. It…

We derive the monotonicity of the quantum relative entropy by an elementary operational argument based on Stein's lemma in quantum hypothesis testing. For the latter we present an elementary and short proof that requires the law of large…

Matrix versions of some basic convexity inequalities are given. Further results on the same topic are proved in the recent papers on arxiv: 1. Hermitian operators and convex functions, 2. A concavity inequality for symmetric norms, 3.…

In information theory, the well-known log-sum inequality is a fundamental tool which indicates the non-negativity for the relative entropy. In this article, we establish a set of inequalities which are similar to the log-sum inequality…

Mercer inequality for convex functions is a variant of Jensen's inequality, with an operator version that is still valid without operator convexity. This paper is two folded. First, we present a Mercer-type inequality for operators without…

The goal of the present paper is to derive some conditions on saturation of (strong) subadditivity inequality for the stochastic matrices. The notion of relative entropy of stochastic matrices is introduced by mimicking quantum relative…

In this article, we prove that convex functions and log-convex functions obey certain general refinements that lead to several refinements and reverses of well known inequalities for matrices, including Young's inequality, Heinz inequality,…