{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:49:26Z","timestamp":1760237366178,"version":"build-2065373602"},"reference-count":10,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,4,3]],"date-time":"2020-04-03T00:00:00Z","timestamp":1585872000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100005357","name":"Slovak Research and Development Agency","doi-asserted-by":"publisher","award":["SK-FR-2017-0002"],"award-info":[{"award-number":["SK-FR-2017-0002"]}],"id":[{"id":"10.13039\/501100005357","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003193","name":"Ministerstvo \u0161kolstva, vedy, v\u00fdskumu a \u0161portu Slovenskej republiky","doi-asserted-by":"publisher","award":["VEGA 2\/0004\/20"],"award-info":[{"award-number":["VEGA 2\/0004\/20"]}],"id":[{"id":"10.13039\/501100003193","id-type":"DOI","asserted-by":"publisher"}]},{"name":"PHC Stefanik","award":["2018\/40494ZJ"],"award-info":[{"award-number":["2018\/40494ZJ"]}]},{"name":"ISITE-BFC","award":["ANR-15-IDEX-03"],"award-info":[{"award-number":["ANR-15-IDEX-03"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Given the fact that the three-qubit symplectic polar space features three different kinds of observables and each of its labeled Fano planes acquires a definite sign, we found that there are 45 distinct types of Mermin pentagrams in this space. A key element of our classification is the fact that any context of such pentagram is associated with a unique (positive or negative) Fano plane. Several intriguing relations between the character of pentagrams\u2019 three-qubit observables and \u2018valuedness\u2019 of associated Fano planes are pointed out. In particular, we find two distinct kinds of negative contexts and as many as four positive ones.<\/jats:p>","DOI":"10.3390\/sym12040534","type":"journal-article","created":{"date-parts":[[2020,4,9]],"date-time":"2020-04-09T03:40:19Z","timestamp":1586403619000},"page":"534","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Taxonomy of Three-Qubit Mermin Pentagrams"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9642-5879","authenticated-orcid":false,"given":"Metod","family":"Saniga","sequence":"first","affiliation":[{"name":"Astronomical Institute of the Slovak Academy of Sciences, SK-05960 Tatransk\u00e1 Lomnica, Slovakia"}]},{"given":"Fr\u00e9d\u00e9ric","family":"Holweck","sequence":"additional","affiliation":[{"name":"Laboratoire Interdisciplinaire Carnot de Bourgogne, ICB\/UTBM, UMR 6303 CNRS, Universit\u00e9 Bourgogne Franche-Comt\u00e9, F-90010 Belfort, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9852-1223","authenticated-orcid":false,"given":"Hamza","family":"Jaffali","sequence":"additional","affiliation":[{"name":"Institut FEMTO-ST, Universit\u00e9 Bourgogne Franche-Comt\u00e9, UTBM, F-90010 Belfort, France"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"803","DOI":"10.1103\/RevModPhys.65.803","article-title":"Hidden variables and the two theorems of John Bell","volume":"65","author":"Mermin","year":"1993","journal-title":"Rev. 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Lett."},{"unstructured":"Cameron, P.J. (1992). Projective and Polar Spaces. QMW Maths Notes, 13, School of Mathematical Sciences, Queen Mary and Westfield College.","key":"ref_6"},{"key":"ref_7","first-page":"96","article-title":"Factor-group-generated polar spaces and (multi-)qudits","volume":"5","author":"Havlicek","year":"2009","journal-title":"Symmetry Integr. Geom. Methods Appl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"60005","DOI":"10.1209\/0295-5075\/86\/60005","article-title":"The geometry of generalized Pauli operators of N-qudit Hilbert space","volume":"86","author":"Thas","year":"2009","journal-title":"EPL Europhys. Lett."},{"unstructured":"Planat, M. Personal Communication.","key":"ref_9"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"224008","DOI":"10.1088\/0264-9381\/29\/22\/224008","article-title":"The black-hole\/qubit correspondence: an up-to-date review","volume":"29","author":"Borsten","year":"2012","journal-title":"Class. Quantum Gravity"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/4\/534\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:15:14Z","timestamp":1760174114000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/4\/534"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,3]]},"references-count":10,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,4]]}},"alternative-id":["sym12040534"],"URL":"https:\/\/doi.org\/10.3390\/sym12040534","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2020,4,3]]}}}