Remark on the additivity conjecture for the quantum depolarizing channel

We consider bistochastic quantum channels generated by unitary representations of the discret group. The proof of the additivity conjecture for the quantum depolarizing channel $\Phi$ based on the decreasing property of the relative entropy is given. We show that the additivity conjecture is true for the channel $\Xi =\Psi \circ \Phi$, where $\Psi$ is the phase damping.