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Open Quantum Systems Decoherence Quantum Simulation Entanglement Theory Quantum Correlations Quantum State Preparation Representation

Entanglement-symmetries of covariant channels

arXiv
Authors: Dominic Verdon

Year

2020

Paper ID

18548

Status

Preprint

Abstract Read

~2 min

Abstract Words

100

Citations

N/A

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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  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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  • 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.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2012.05761 [2] arXiv https://arxiv.org/abs/2012.05761 [3] Publisher https://arxiv.org/abs/2012.05761

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