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arXiv · 2012.05761

Entanglement-symmetries of covariant channels

Dominic Verdon
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Abstract

Let G and G' be monoidally equivalent compact quantum groups, and let H be a Hopf-Galois object realising a monoidal equivalence between these groups' representation categories. This monoidal equivalence induces an equivalence Chan(G) -> Chan(G'), where Chan(G) is the category whose objects are finite-dimensional C*-algebras with an action of G and whose morphisms are covariant channels. We show that, if the Hopf-Galois object H has a finite-dimensional *-representation, then channels related by this equivalence can simulate each other using a finite-dimensional entangled resource. We use this result to calculate the entanglement-assisted capacities of certain quantum channels.

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BibTeXRIS

Dominic Verdon. 2020-12-10. Entanglement-symmetries of covariant channels. https://doi.org/10.22331/q-2024-02-29-1272

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