{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T09:04:40Z","timestamp":1773479080371,"version":"3.50.1"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2022,9,12]],"date-time":"2022-09-12T00:00:00Z","timestamp":1662940800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>In a recent paper, a realizability technique has been used to give a\nsemantics of a quantum lambda calculus. Such a technique gives rise to an\ninfinite number of valid typing rules, without giving preference to any subset\nof those. In this paper, we introduce a valid subset of typing rules, defining\nan expressive enough quantum calculus. Then, we propose a categorical semantics\nfor it. Such a semantics consists of an adjunction between the category of\ndistributive-action spaces of value distributions (that is, linear combinations\nof values in the lambda calculus), and the category of sets of value\ndistributions.<\/jats:p>","DOI":"10.46298\/lmcs-18(3:32)2022","type":"journal-article","created":{"date-parts":[[2022,9,19]],"date-time":"2022-09-19T07:35:37Z","timestamp":1663572937000},"source":"Crossref","is-referenced-by-count":5,"title":["Quantum Control in the Unitary Sphere: Lambda-S1 and its Categorical Model"],"prefix":"10.46298","volume":"Volume 18, Issue 3","author":[{"given":"Alejandro","family":"D\u00edaz-Caro","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Octavio","family":"Malherbe","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2022,9,12]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/10027\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/10027\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T20:19:50Z","timestamp":1687292390000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/7408"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,12]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-18(3:32)2022","relation":{"has-preprint":[{"id-type":"arxiv","id":"2012.05887v4","asserted-by":"subject"},{"id-type":"arxiv","id":"2012.05887v3","asserted-by":"subject"},{"id-type":"arxiv","id":"2012.05887v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2012.05887","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2012.05887","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,12]]},"article-number":"7408"}}