New Constructive Counterexamples to Additivity of Minimum Output Rényi p-Entropy of Quantum Channels

Abstract

In this paper, we present new families of quantum channels for which corresponding minimum output Rényi p-entropy is not additive. Our manuscript is motivated by the results of Grudka et al. 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 $p\gt 2$ .