Quantum relative entropy: general convergence criterion and preservation of convergence under completely positive linear maps

TL;DR

This paper establishes a criterion for the convergence of quantum relative entropy and demonstrates that this convergence is preserved under completely positive linear maps, with applications to quantum information theory.

Contribution

It introduces a new criterion for quantum relative entropy convergence and proves its preservation under certain quantum operations, advancing understanding in quantum information theory.

Findings

Established a convergence criterion for quantum relative entropy.

Proved preservation of local continuity under completely positive maps.

Discussed applications in quantum information processing.

Abstract

A criterion and necessary conditions for convergence (local continuity) of the quantum relative entropy are obtained. Some applications of these results are considered. In particular, the preservation of local continuity of the quantum relative entropy under completely positive linear maps is established.