On Weyl channels being covariant with respect to the maximum commutative group of unitaries

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.Comment: A completely revised version, 20 page

Transmitting qudits through larger quantum channels

We address the problem of transmitting states belonging to finite dimensional Hilbert space through a quantum channel associated with a larger (even infinite dimensional) Hilbert space.Comment: 5 pages, ReVTeX, minor changes, to appear in J. Phys.