Constructive counterexamples to additivity of minimum output R\'enyi entropy of quantum channels for all p>2

TL;DR

This paper provides explicit counterexamples showing that the minimum output Rb4enyi entropy of quantum channels is not additive for all p>2, using antisymmetric subspaces, and discusses extensions to other p values.

Contribution

The paper introduces a constructive method to demonstrate non-additivity of minimum output Rb4enyi entropy for quantum channels for all p>2, expanding understanding of quantum information properties.

Findings

Counterexamples for p>2 using antisymmetric subspaces

Discussion on potential extension to p=0 and entanglement breaking channels

Evidence that additivity does not hold universally for all p>2

Abstract

We present a constructive example of violation of additivity of minimum output R\'enyi entropy for each p>2. The example is provided by antisymmetric subspace of a suitable dimension. We discuss possibility of extension of the result to go beyond p>2 and obtain additivity for p=0 for a class of entanglement breaking channels.