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Communications in Mathematical Physics

, Volume 289, Issue 3, pp 1057–1086 | Cite as

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

Open Access
Article

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.

Keywords

Convex Hull Extreme Point Entangle State Quantum Channel Convex Combination 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Max-Planck-Institute for Quantum OpticsGarchingGermany
  2. 2.Niels Bohr InstituteCopenhagenDenmark

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