{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T00:57:50Z","timestamp":1775091470088,"version":"3.50.1"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2005,6]]},"abstract":"<jats:p> A complete set of N + 1 mutually unbiased bases (MUBs) forms a convex polytope in the N<jats:sup>2<\/jats:sup> - 1 dimensional space of N \u00d7 N Hermitian matrices of unit trace. As a geometrical object such a polytope exists for all values of N, while it is unknown whether it can be made to lie within the body of density matrices unless N = p<jats:sup>k<\/jats:sup>, where p is prime. We investigate the polytope in order to see if some values of N are geometrically singled out. One such feature is found: It is possible to select N<jats:sup>2<\/jats:sup> facets in such a way that their centers form a regular simplex if and only if there exists an affine plane of order N. Affine planes of order N are known to exist if N = p<jats:sup>k<\/jats:sup>; perhaps they do not exist otherwise. However, the link to the existence of MUBs \u2014 if any \u2014 remains to be found. <\/jats:p>","DOI":"10.1007\/s11080-005-5721-3","type":"journal-article","created":{"date-parts":[[2005,5,31]],"date-time":"2005-05-31T17:09:51Z","timestamp":1117559391000},"page":"107-120","source":"Crossref","is-referenced-by-count":35,"title":["Mutually Unbiased Bases and the Complementarity Polytope"],"prefix":"10.1142","volume":"12","author":[{"given":"Ingemar","family":"Bengtsson","sequence":"first","affiliation":[{"name":"Fysikum, Stockholms Universitet, S-106 91 Stockholm, Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"\u00c5sa","family":"Ericsson","sequence":"additional","affiliation":[{"name":"Fysikum, Stockholms Universitet, S-106 91 Stockholm, Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,4,17]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4916(89)90322-9"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/14\/12\/019"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4916(87)90176-X"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1002\/9781118032565"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/36\/39\/310"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.17.1249"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1063\/1.1737053"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.65.032320"},{"key":"rf18","first-page":"512","volume":"34","author":"Bandyopadhyay S.","journal-title":"Algorithmica"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1088\/1464-4266\/6\/9\/L01"}],"container-title":["Open Systems &amp; Information Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1007\/s11080-005-5721-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T04:38:14Z","timestamp":1565152694000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1007\/s11080-005-5721-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,6]]},"references-count":10,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2012,4,17]]},"published-print":{"date-parts":[[2005,6]]}},"alternative-id":["10.1007\/s11080-005-5721-3"],"URL":"https:\/\/doi.org\/10.1007\/s11080-005-5721-3","relation":{},"ISSN":["1230-1612","1793-7191"],"issn-type":[{"value":"1230-1612","type":"print"},{"value":"1793-7191","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,6]]}}}