  The notion of potential output purity of a completely positive map is
introduced as a generalization of the regularized output purity. An upper bound
is derived for this quantity, and for several classes of maps (including CQ, QC
and Hadamard channels) it is shown that potential purity does not exceed the
standard output purity. As an application the potential purity is used to bound
the logarithmic Sobolev constant of a product of depolarizing channel
semigroups.
