Calculation of classical capacity for quantum channels generated by irreducible projective unitary representations of finite groups

The quantum coding theorem proved by A.S. Holevo and independently by B. Schumacher and M.D. Westmoreland in 1996 gives an upper bound on the number of quantum states (positive operators with a unit trace) which can be used in encoding to transmit information in parallel via $m$ copies of the channel when $m$ tends to infinity. Such an estimate includes a constant $C$, called a classical capacity of the channel. Computing $C$ presents considerable technical complexity. We consider quantum channels, which are convex combinations of actions of unitary operators of an irreducible projective unitary representation of some finite group $G$, determined by the probability distribution on $G$. Assuming that the projective unitary representation is obtained by the continuation of the unitary representation of the Abelian normal subgroup $T$ of group $G$, applying the majorization condition on the probability distribution, the classical capacity of the channel is found.