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.
- 14.Watrous, J.: Mixing doubly stochastic quantum channels with the completely depolarizing channel. http://arXiv.org/abs/0807.2668v1[quant-ph], 2008
- 21.DiVincenzo, D.P., Fuchs, C.A., Mabuchi, H., Smolin, J.A., Thapliyal, A.V., Uhlmann, A.: Entanglement of assistance. In: Proc. Quantum Computing and Quantum Communications, First NASA Intl. Conf., Palm Springs, Berlin-Heidelberg-New York: Springer, 1999, pp. 247–257Google Scholar
- 26.Open problems in QIT. http://www.imaph.tu-bs.de/qi/problems/