  Let $\Phi$ be a trace-preserving, positivity-preserving (but not necessarily
completely positive) linear map on the algebra of complex $2 \times 2$
matrices, and let $\Omega$ be any finite-dimensional completely positive map.
For $p=2$ and $p \geq 4$, we prove that the maximal $p$-norm of the product map
$\Phi \ot \Omega$ is the product of the maximal $p$-norms of $\Phi$ and
$\Omega$. Restricting $\Phi$ to the class of completely positive maps, this
settles the multiplicativity question for all qubit channels in the range of
values $p \geq 4$.
