Multiplicativity of superoperator norms for some entanglement breaking channels

It is known that the minimal output entropy is additive for any product of entanglement breaking (EB) channels. The same is true for the Renyi entropy, where additivity is equivalent to multiplicativity of the $1\to q$ norm for all $q\ge 1$. In this paper we consider the related question of multiplicativity of the $2\to q$ norm for entanglement breaking channels. We prove that multiplicativity holds in this case for certain classes of EB channels, including both the CQ and QC channels.