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The are several non-equivalent notions of Markovian quantum evolution. Inthis paper we show that the one based on the so-called CP-divisibility of thecorresponding dynamical map enjoys the following stability property: thedynamical map $\Lambda_t$ is CP-divisible iff the second tensor power$\Lambda_t\otimes\Lambda_t$ is CP-divisible as well. Moreover, theP-divisibility of the map $\Lambda_t\otimes\Lambda_t$ is equivalent to theCP-divisibility of the map $\Lambda_t$. Interestingly, the latter property isno 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 completepositivity. That is, unlike when $\Lambda_t$ has a time-independent generator,positivity of $\Lambda_t\otimes\Lambda_t$ does not imply complete positivity of$\Lambda_t$.

Tensor power of dynamical maps and P- vs. CP-divisibility