{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:13:50Z","timestamp":1760210030055,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2017,12,31]],"date-time":"2017-12-31T00:00:00Z","timestamp":1514678400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>It has been shown in previous papers that classes of (minimal asymmetric) informationally-complete positive operator valued measures (IC-POVMs) in dimension d can be built using the multiparticle Pauli group acting on appropriate fiducial states. The latter states may also be derived starting from the Poincar\u00e9 upper half-plane model    H   . To do this, one translates the congruence (or non-congruence) subgroups of index d of the modular group into groups of permutation gates, some of the eigenstates of which are the sought fiducials. The structure of some IC-POVMs is found to be intimately related to the Kochen\u2013Specker theorem.<\/jats:p>","DOI":"10.3390\/e20010016","type":"journal-article","created":{"date-parts":[[2018,1,3]],"date-time":"2018-01-03T12:00:06Z","timestamp":1514980806000},"page":"16","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["The Poincar\u00e9 Half-Plane for Informationally-Complete POVMs"],"prefix":"10.3390","volume":"20","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"}]}],"member":"1968","published-online":{"date-parts":[[2017,12,31]]},"reference":[{"key":"ref_1","unstructured":"Ghesquier, M.-F. (2014). 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