Operator algebra generalization of a theorem of Watrous and mixed unitary quantum channels - Archive ouverte HAL
Article Dans Une Revue Journal of Physics A: Mathematical and Theoretical Année : 2024

Operator algebra generalization of a theorem of Watrous and mixed unitary quantum channels

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e establish an operator algebra generalization of Watrous' theorem (Watrous 2009 Quantum Inf. Comput. 9 403–413) 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.
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hal-04390457 , version 1 (22-10-2024)

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David Kribs, Jeremy Levick, Rajesh Pereira, Mizanur Rahaman. Operator algebra generalization of a theorem of Watrous and mixed unitary quantum channels. Journal of Physics A: Mathematical and Theoretical, 2024, 57, pp.115303. ⟨10.1088/1751-8121/ad2cb0⟩. ⟨hal-04390457⟩
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