Unital Quantum Channels – Convex Structure and Revivals of Birkhoff’s Theorem

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 characte...

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Bibliographic Details
Published in:Communications in mathematical physics 2009-08, Vol.289 (3), p.1057-1086
Main Authors: Mendl, Christian B., Wolf, Michael M.
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary: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.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-009-0824-2