  We investigate the Weyl channels being covariant with respect to the maximum
commutative group of unitary operators. This class includes the quantum
depolarizing channel and the "two-Pauli" channel as well. Then, we show that
our estimation of the output entropy for a tensor product of the phase damping
channel and the identity channel based upon the decreasing property of the
relative entropy allows to prove the additivity conjecture for the minimal
output entropy for the quantum depolarizing channel in any prime dimesnsion and
for the "two Pauli" channel in the qubit case.
