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This monoidal equivalence induces an equivalence Chan(<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>G<\/mml:mi><\/mml:math>) <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mo stretchy=\"false\">&amp;#x2192;<\/mml:mo><\/mml:math> Chan(<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msup><mml:mi>G<\/mml:mi><mml:mo>&amp;#x2032;<\/mml:mo><\/mml:msup><\/mml:math>), where Chan(<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>G<\/mml:mi><\/mml:math>) is the category whose objects are finite-dimensional <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>C<\/mml:mi><mml:mo>&amp;#x2217;<\/mml:mo><\/mml:math>-algebras with an action of G and whose morphisms are covariant channels. We show that, if the Hopf-Galois object <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>H<\/mml:mi><\/mml:math> 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.<\/jats:p>","DOI":"10.22331\/q-2024-02-29-1272","type":"journal-article","created":{"date-parts":[[2024,2,29]],"date-time":"2024-02-29T15:37:22Z","timestamp":1709221042000},"page":"1272","update-policy":"http:\/\/dx.doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":2,"title":["Entanglement-symmetries of covariant channels"],"prefix":"10.22331","volume":"8","author":[{"given":"Dominic","family":"Verdon","sequence":"first","affiliation":[{"name":"School of Mathematics, University of Bristol"}]}],"member":"9598","published-online":{"date-parts":[[2024,2,29]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Samson Abramsky and Bob Coecke. A categorical semantics of quantum protocols. In Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004., pages 415\u2013425. 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