  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.
