We present some results and examples on the mixed unitary rank $m$ of a mixed unitary channel $\Phi$, that is the minimal number of unitaries $U_i$ such that $\Phi$ can be written in Choi-Kraus form by means of the $U_i$.

We present an upper bound on $m$ in terms of the Choi rank and the dimension of the usual operator system associated to $\Phi$, and exhibit a class of examples based on mutually unbiased bases with large gap between the Choi rank and mixed unitary rank.