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

By Christian B. Mendl, Michael M. Wolf. 2008

150 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/141900c24c4489165db03a7eb5924fc71065808e

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

In Electrical and Electronic Engineering

Citations in the corpus

The Mathematical Language of Quantum Theory: From Uncertainty to Entanglement (2012, background): “We refer to [8], [98] for further details on the connection between these two classes of channels.”
Geometry of Quantum States: Index (2007, background): “Computable criteria, which allow one to identify bistochastic maps which are not mixtures of unitaries, were given by Mendl and Wolf [653].”
The resource theory of informational nonequilibrium in thermodynamics (2013, background): “Recall that a unital operation E : L(Hin) → L(Hout) is one for which E(1in/din) = 1out/dout, where 1in and 1out are the identity operators on Hin and Hout, respectively (Mendl and Wolf, 2009).”
An Asymptotic Property of Factorizable Completely Positive Maps and the Connes Embedding Problem (2014, methodology): “The value λ0 is not stated explicitly in [9], but following the details of their proof one can show (see Remark 6.”