  The study of open quantum systems relies on the notion of unital completely
positive semigroups on $C^*$-algebras representing physical systems. The
natural generalisation would be to consider the unital completely positive
semigroups on operator systems. We show that any continuous unital completely
positive semigroup on matricial system can be extended to a semigroup on a
finite-dimensional $C^*$-algebra, which is an injective envelope of the
matricial system. In case the semigroup is invertible, this extension is
unique.
