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

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

2008-06-17

arxiv.org/abs/0806.2820v1

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

Physics

Quantum Physics

31 pages

Scientific paper

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.

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