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It is conjectured that the Holevo capacity of a product channel \Omega\otimes \Phi is achieved when product states are used as input. Amosov, Holevoand Werner have also conjectured that the maximal p-norm of a product channelis achieved with product input states. In this paper we establish both of theseconjectures in the case that \Omega is arbitrary and \Phi is a CQ or QC channel(as defined by Holevo). We also establish the Amosov, Holevo and Wernerconjecture when \Omega is arbitrary and either \Phi is a qubit channel and p=2,or \Phi is a unital qubit channel and p is integer. Our proofs involve a newconjecture for the norm of an output state of the half-noisy channel I \otimes\Phi, when \Phi is a qubit channel. We show that this conjecture in some casesalso implies additivity of the Holevo capacity

Maximization of capacity and lp norms for some product channels