New Perspectives and some Celebrated Quantum Inequalities

TL;DR

This paper explores quantum entropy inequalities using matrix perspectives and operator convex functions, providing new algebraic insights and extending known inequalities like Lieb's $p+q\

Contribution

It introduces a general framework for deriving quantum entropy inequalities via matrix perspectives and operator convexity, extending classical results.

Findings

Derived new quantum entropy inequalities from matrix perspectives.

Extended Lieb's inequality to broader contexts.

Provided algebraic proofs for celebrated quantum inequalities.

Abstract

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. A matrix analogue of Mar\'{e}chal's extended perspectives provides additional inequalities, including a $p+q\leq 1$ result of Lieb.