  We establish an operator algebra generalization of Watrous' theorem
\cite{watrous2009} on mixing unital quantum channels (completely positive
trace-preserving maps) with the completely depolarizing channel, wherein the
more general objects of focus become (finite-dimensional) von Neumann algebras,
the unique trace preserving conditional expectation onto the algebra, the group
of unitary operators in the commutant of the algebra, and the fixed point
algebra of the channel. As an application, we obtain a result on the asymptotic
theory of quantum channels, showing that all unital channels are eventually
mixed unitary. We also discuss the special case of the diagonal algebra in
detail, and draw connections to the theory of correlation matrices and Schur
product maps.
