Remark on the Additivity Conjecture for a Quantum Depolarizing Channel

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