{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:55:20Z","timestamp":1760237720926,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2020,6,11]],"date-time":"2020-06-11T00:00:00Z","timestamp":1591833600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A popular account of the mixing patterns for the three generations of quarks and leptons is through the characters    \u03ba    of a finite group G. Here, we introduce a d-dimensional Hilbert space with     d = c c ( G )    , the number of conjugacy classes of G. Groups under consideration should follow two rules, (a) the character table contains both two- and three-dimensional representations with at least one of them faithful and (b) there are minimal informationally complete measurements under the action of a d-dimensional Pauli group over the characters of these representations. Groups with small d that satisfy these rules coincide in a large part with viable ones derived so far for reproducing simultaneously the CKM (quark) and PNMS (lepton) mixing matrices.<\/jats:p>","DOI":"10.3390\/sym12061000","type":"journal-article","created":{"date-parts":[[2020,6,16]],"date-time":"2020-06-16T00:50:49Z","timestamp":1592268649000},"page":"1000","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Informationally Complete Characters for Quark and Lepton Mixings"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5739-546X","authenticated-orcid":false,"given":"Michel","family":"Planat","sequence":"first","affiliation":[{"name":"Institut FEMTO-ST CNRS UMR 6174, Universit\u00e9 de Bourgogne\/Franche-Comt\u00e9, 15 B Avenue des Montboucons, F-25044 Besan\u00e7on, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6953-8202","authenticated-orcid":false,"given":"Raymond","family":"Aschheim","sequence":"additional","affiliation":[{"name":"Quantum Gravity Research, Los Angeles, CA 90290, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0637-1916","authenticated-orcid":false,"given":"Marcelo M.","family":"Amaral","sequence":"additional","affiliation":[{"name":"Quantum Gravity Research, Los Angeles, CA 90290, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2938-3941","authenticated-orcid":false,"given":"Klee","family":"Irwin","sequence":"additional","affiliation":[{"name":"Quantum Gravity Research, Los Angeles, CA 90290, USA"}]}],"member":"1968","published-online":{"date-parts":[[2020,6,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ramond, P. 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