Entanglement-symmetries Of Covariant Channels

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Dominic Verdon

School of Mathematics, University of Bristol

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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($G$) $rightarrow$ 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.

► BibTeX data

@article{Verdon2024entanglement, doi = {10.22331/q-2024-02-29-1272}, url = {https://doi.org/10.22331/q-2024-02-29-1272}, title = {Entanglement-symmetries of covariant channels}, author = {Verdon, Dominic}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {8}, pages = {1272}, month = feb, year = {2024} }

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Cited by

[1] Dominic Verdon, “A covariant Stinespring theorem”, Journal of Mathematical Physics 63 9, 091705 (2022).

[2] Dominic Verdon, “Entanglement-invertible channels”, arXiv:2204.04493, (2022).

[3] Dominic Verdon, “Unitary transformations of fibre functors”, arXiv:2004.12761, (2020).

[4] Dominic Verdon, “Covariant Quantum Combinatorics with Applications to Zero-Error Communication”, Communications in Mathematical Physics 405 2, 51 (2024).

The above citations are from SAO/NASA ADS (last updated successfully 2024-03-01 15:39:39). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2024-03-01 15:39:37).

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.

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Source: https://quantum-journal.org/papers/q-2024-02-29-1272/

Time Stamp: February 29, 2024

Time Stamp: Jan 4, 2024

Republished By Plato

Abstract

► BibTeX data

► References

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