  We study unital quantum channels which are obtained via partial trace of a
$*$-automorphism of a finite unital matrix $*$-algebra. We prove that any such
channel, $q$, on a unital matrix $*$-algebra, $\mathcal{A}$, admits a finite
matrix $N-$dilation, $\alpha _N$, for any natural number N. Namely, $\alpha _N$
is a $*$-automorphism of a larger bi-partite matrix algebra $\mathcal{A}
\otimes \mathcal{B}$ so that partial trace of $M$-fold self-compositions of
$\alpha _N$ yield the $M$-fold self-compositions of the original quantum
channel, for any $1\leq M \leq N$. This demonstrates that repeated applications
of the channel can be viewed as $*$-automorphic time evolution of a larger
finite quantum system.
