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

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 $p>2$.