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Unital Quantum Channels - Convex Structure and Revivals of Birkhoff's Theorem

Christian B. Mendl, Michael M. Wolf

Commun. Math. Phys. 289, 1057-1096 **, (2009) 0806.2820 Pfeil

Abstract: The set of doubly-stochastic quantum channels and its subset of mixtures of unitaries are investigated. We provide a detailed analysis of their structure together with computable criteria for the separation of the two sets. When applied to O(d)-covariant channels this leads to a complete characterization and reveals a remarkable feature: instances of channels which are not in the convex hull of unitaries can return to it when either taking finitely many copies of them or supplementing with a completely depolarizing channel. In these scenarios this implies that a channel whose noise initially resists any environment-assisted attempt of correction can become perfectly correctable.