  In this paper we present new families of quantum channels for which
corresponding minimum output R\'{e}nyi entropy is not additive. In the first
part of the manuscript, motivated by work of Grudka et. al. (J. Phys. A: Math.
Theor. 43, 425304 (2010)), we focus on extensions of the antisymmetric space
and its subspaces. Later on we analyze a special case of completely entangled
subspace proposed by Parthasarathy in Proc. Math. Sci. 114, 365-374 (2004). Our
construction works for every $p>2$ and dimension high enough.
