Entanglement-symmetries of covariant channels
arXiv:2012.05761 · doi:10.22331/q-2024-02-29-1272
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.
arXiv comment34 pages, many coloured pictures | Rev 10: Included missing funder information
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