Continuity of the relative entropy of resource

TL;DR

This paper establishes a criterion for the local continuity of the relative entropy of resource, with applications to multipartite entanglement and quantum mutual information.

Contribution

It introduces a new criterion for local continuity of the relative entropy of resource and explores its implications for multipartite entanglement.

Findings

Criterion for local continuity of relative entropy of resource

Continuity of multipartite entanglement relates to quantum mutual information

Applications to relative entropy of entanglement in multipartite systems

Abstract

A criterion of local continuity of the relative entropy of resource -- the relative entropy distance to the set of free states -- is obtained. Several basic corollaries of this criterion are presented. Applications to the relative entropy of entanglement in multipartite quantum systems are considered. It is shown, in particular, that local continuity of any relative entropy of multipartite entanglement follows from local continuity of the quantum mutual information.