New constructive counterexamples to additivity of minimum output R\'enyi p-entropy of quantum channels

TL;DR

This paper introduces new quantum channels based on antisymmetric subspaces where the minimum output Rb5nyi p-entropy is shown to be non-additive for p>2, challenging previous assumptions in quantum information theory.

Contribution

The authors construct novel families of quantum channels that demonstrate non-additivity of the minimum output Rb5nyi p-entropy for p>2, expanding understanding of entropy behavior in quantum channels.

Findings

Identified channels with non-additive minimum output Rb5nyi p-entropy for p>2

Extended previous results by focusing on antisymmetric subspaces

Provided explicit examples of additivity breaking in quantum channels

Abstract

In this paper, we present new families of quantum channels for which corresponding minimum output R\'enyi $p$-entropy is not additive. Our manuscript is motivated by the results of Grudka et al., J. Phys. A: Math. Theor. 43 425304 and we focus on channels characterized by both extensions and subspaces of the antisymmetric subspace in $\mathbb{C}^d \otimes \mathbb{C}^d$, which exhibit additivity breaking for $p>2$.