Entanglement-symmetries of covariant channels - Dominic Verdon (Quantum, 2024)
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.