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 become elements of this set by either taking two copies of them or supplementing with a completely depolarizing channel. These scenarios imply that a channel whose noise initially resists any environment-assisted attempt of correction can become perfectly correctable.
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Communicated by M.B. Ruskai
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Mendl, C.B., Wolf, M.M. Unital Quantum Channels – Convex Structure and Revivals of Birkhoff’s Theorem. Commun. Math. Phys. 289, 1057–1086 (2009). https://doi.org/10.1007/s00220-009-0824-2
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DOI: https://doi.org/10.1007/s00220-009-0824-2
Keywords
- Convex Hull
- Extreme Point
- Entangle State
- Quantum Channel
- Convex Combination