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It is well-known that such a device is impossible with a finite-dimensional program register for any set that contains infinitely many unitary quantum channels (Nielsen and Chuang's <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mtext class=\"MJX-tex-mathit\" mathvariant=\"italic\">No-Programming Theorem<\/mml:mtext><\/mml:mrow><\/mml:math>), meaning that a universal programmable quantum processor does not exist. The situation changes if the system has symmetries. Indeed, here we consider group-covariant channels. If the group acts irreducibly on the channel input, these channels can be implemented exactly by a programmable quantum processor with finite program dimension (via <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mtext class=\"MJX-tex-mathit\" mathvariant=\"italic\">teleportation simulation<\/mml:mtext><\/mml:mrow><\/mml:math>, which uses the Choi-Jamiolkowski state of the channel as a program). Moreover, by leveraging the representation theory of the symmetry group action, we show how to remove redundancy in the program and prove that the resulting program register has minimum Hilbert space dimension. Furthermore, we provide upper and lower bounds on the program register dimension of a processor implementing all group-covariant channels approximately.<\/jats:p>","DOI":"10.22331\/q-2021-06-29-488","type":"journal-article","created":{"date-parts":[[2021,6,29]],"date-time":"2021-06-29T15:43:13Z","timestamp":1624981393000},"page":"488","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":12,"title":["Programmability of covariant quantum channels"],"prefix":"10.22331","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2155-9693","authenticated-orcid":false,"given":"Martina","family":"Gschwendtner","sequence":"first","affiliation":[{"name":"Munich Center for Quantum Science and Technology (MCQST), 80799 M\u00fcnchen, Germany"},{"name":"Zentrum Mathematik, Technical University of Munich, 85748 Garching, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4796-7633","authenticated-orcid":false,"given":"Andreas","family":"Bluhm","sequence":"additional","affiliation":[{"name":"QMATH, Department of Mathematical Sciences, University of Copenhagen, 2100 Copenhagen, Denmark"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6344-4870","authenticated-orcid":false,"given":"Andreas","family":"Winter","sequence":"additional","affiliation":[{"name":"Instituci\u00f3 Catalana de Recerca i Estudis Avan\u00e7ats (ICREA), Pg. 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