Unital Quantum Channels – Convex Structure and Revivals of Birkhoff’s Theorem |
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Authors: | Christian B Mendl Michael M Wolf |
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Institution: | (1) Max-Planck-Institute for Quantum Optics, Garching, Germany;(2) Niels Bohr Institute, Copenhagen, Denmark |
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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. |
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