{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:12:24Z","timestamp":1760242344275,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2017,5,11]],"date-time":"2017-05-11T00:00:00Z","timestamp":1494460800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004055","name":"King Fahd University of Petroleum and Minerals","doi-asserted-by":"publisher","award":["SR141007"],"award-info":[{"award-number":["SR141007"]}],"id":[{"id":"10.13039\/501100004055","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001711","name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","doi-asserted-by":"publisher","award":["PBZHP2-147294"],"award-info":[{"award-number":["PBZHP2-147294"]}],"id":[{"id":"10.13039\/501100001711","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We apply the geometric quantization procedure via symplectic groupoids to the setting of epistemically-restricted toy theories formalized by Spekkens (Spekkens, 2016). In the continuous degrees of freedom, this produces the algebraic structure of quadrature quantum subtheories. In the odd-prime finite degrees of freedom, we obtain a functor from the Frobenius algebra of the toy theories to the Frobenius algebra of stabilizer quantum mechanics.<\/jats:p>","DOI":"10.3390\/e19050220","type":"journal-article","created":{"date-parts":[[2017,5,11]],"date-time":"2017-05-11T11:06:46Z","timestamp":1494500806000},"page":"220","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Functorial Construction of Quantum Subtheories"],"prefix":"10.3390","volume":"19","author":[{"given":"Ivan","family":"Contreras","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Illinois at Urbana-Champain, Urbana, IL 61801, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1299-8571","authenticated-orcid":false,"given":"Ali","family":"Duman","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,5,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1142\/S0129055X05002376","article-title":"Quantization methods: A guide for physicist and analyst","volume":"17","author":"Ali","year":"2005","journal-title":"Rev. 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