New constructive counterexamples to additivity of minimum output Rényi p-entropy of quantum channels

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., 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 $p>2$.