Unital quantum channels - Convex structure and revivals of Birkhoff's theorem

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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.

Original languageEnglish
Pages (from-to)1057-1086
Number of pages30
JournalCommunications in Mathematical Physics
Issue number3
StatePublished - Aug 2009
Externally publishedYes


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