  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.
