  Finite-time Markovian channels, unlike their infinitesimal counterparts, do
not form a convex set. As a particular instance of this observation, we
consider the problem of mixing the three Pauli channels, conservatively assumed
to be quantum dynamical semigroups, and fully characterize the resulting
``Pauli simplex.'' We show that neither the set of non-Markovian (completely
positive indivisible) nor Markovian channels is convex in the Pauli simplex,
and that the measure of non-Markovian channels is about 0.87. All channels in
the Pauli simplex are P divisible. A potential application in the context of
quantum resource theory is also discussed.
