The minimum entropy output of a quantum channel is locally additive

TL;DR

This paper proves that the minimum von-Neumann entropy output of a quantum channel is locally additive, revealing that non-additivity is a global phenomenon contrary to previous expectations.

Contribution

It establishes the local additivity of the minimum entropy output, challenging the belief that non-additivity is inherent to quantum channels.

Findings

Minimum entropy output is locally additive

Non-additivity is a global effect

Counterexample by Hastings is globally non-additive

Abstract

We show that the minimum von-Neumann entropy output of a quantum channel is locally additive. Hasting's counterexample for the additivity conjecture, makes this result quite surprising. In particular, it indicates that the non-additivity of the minimum entropy output is a global effect of quantum channels.