# Simple characterization of positive linear maps preserving continuity of the von Neumann entropy

## TL;DR

This paper characterizes positive linear maps that preserve the local continuity of von Neumann entropy, showing they must also preserve entropy finiteness, which relates to boundedness on pure states.

## Contribution

It provides a precise criterion for when positive linear maps preserve the continuity of von Neumann entropy, linking it to the preservation of entropy finiteness.

## Key findings

- Maps preserving entropy continuity also preserve finiteness of entropy.
- Finiteness preservation is equivalent to boundedness of output entropy on pure states.
- Characterization applies to positive linear maps in quantum information theory.

## Abstract

We show that a positive linear map preserves local continuity (convergence) of the entropy if and only if it preserves finiteness of the entropy, i.e. transforms operators with finite entropy to operators with finite entropy. The last property is equivalent to the boundedness of the output entropy of a map on the set of pure states.