Additivity for unital qubit channels

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Abstract
Additivity of the Holevo capacity is proved for product channels, under the condition that one of the channels is in a certain class of unital qubit channels, with the other completely arbitrary. This qubit class includes the depolarizing channel. As a byproduct this proves that the Holevo bound is the ultimate information capacity of such qubit channels (assuming no prior entanglement between sender and receiver). Additivity of minimal entropy and multiplicativity of p-norms are also proved under the same assumptions