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

Operator Algebra Generalization of a Theorem of Watrous and Mixed Unitary Quantum Channels