  The are several non-equivalent notions of Markovian quantum evolution. In
this paper we show that the one based on the so-called CP-divisibility of the
corresponding dynamical map enjoys the following stability property: the
dynamical map $\Lambda_t$ is CP-divisible iff the second tensor power
$\Lambda_t\otimes\Lambda_t$ is CP-divisible as well. Moreover, the
P-divisibility of the map $\Lambda_t\otimes\Lambda_t$ is equivalent to the
CP-divisibility of the map $\Lambda_t$. Interestingly, the latter property is
no longer true if we replace the P-divisibility of $\Lambda_t\otimes\Lambda_t$
by simple positivity and the CP-divisibility of $\Lambda_t$ by complete
positivity. That is, unlike when $\Lambda_t$ has a time-independent generator,
positivity of $\Lambda_t\otimes\Lambda_t$ does not imply complete positivity of
$\Lambda_t$.
