Communications in Mathematical Physics

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

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

  • Christian B. Mendl
  • Michael M. Wolf
Open Access


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.


Convex Hull Extreme Point Entangle State Quantum Channel Convex Combination 
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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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