The minimum Renyi entropy output of a quantum channel is locally additive

TL;DR

This paper proves that the minimum Renyi entropy output of a quantum channel is locally additive for alpha>1, extending previous results for alpha=1, and introduces new techniques based on p-norms.

Contribution

It establishes local additivity of minimum Renyi entropy output for alpha>1 using novel methods involving p-norms, contrasting with von-Neumann entropy properties.

Findings

Local additivity holds for alpha>1

Counterexamples show global effects in Renyi entropy additivity

New techniques do not extend to alpha<1

Abstract

We show that the minimum Renyi entropy output of a quantum channel is locally additive for Renyi parameter alpha>1. While our work extends the results of [10] (in which local additivity was proven for alpha=1), it is based on several new techniques that incorporate the multiplicative nature of p-norms, in contrast to the additivity property of the von-Neumann entropy. Our results demonstrate that the counterexamples to the Renyi additivity conjectures exhibit global effects of quantum channels. Interestingly, the approach presented here can not be extended to Renyi entropies with parameter alpha<1.