Trace functions with applications in quantum physics

TL;DR

This paper explores trace functions in quantum physics, establishing convexity properties and entropy inequalities using operator monotone functions, and introduces new trace functions with potential applications.

Contribution

It provides new proofs of convexity results for trace functions and introduces novel trace functions relevant to quantum information theory.

Findings

Convexity of residual entropy functions established

Simplified proofs of Carlen-Lieb theorems provided

New trace functions with applications in quantum physics introduced

Abstract

We consider both known and not previously studied trace functions with applications in quantum physics. By using perspectives we obtain convexity statements for different notions of residual entropy, including the entropy gain of a quantum channel as studied by Holevo and others. We give new and simplified proofs of the Carlen-Lieb theorems concerning concavity or convexity of certain trace functions by making use of the theory of operator monotone functions. We then apply these methods in a study of new types of trace functions. Keywords: Trace function, convexity, entropy gain, residual entropy, operator monotone function.