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Dyn."],"published-print":{"date-parts":[[2021,9]]},"abstract":"<jats:p> Suppose that for some unit vectors [Formula: see text] in [Formula: see text] we have that for any [Formula: see text] \u00a0 [Formula: see text] is either orthogonal to [Formula: see text] or [Formula: see text] (i.e., [Formula: see text] and [Formula: see text] are unbiased). We prove that if [Formula: see text], then these vectors necessarily form a complete system of mutually unbiased bases, that is, they can be arranged into [Formula: see text] orthonormal bases, all being mutually unbiased with respect to each other. <\/jats:p>","DOI":"10.1142\/s1230161221500128","type":"journal-article","created":{"date-parts":[[2022,5,13]],"date-time":"2022-05-13T07:12:14Z","timestamp":1652425934000},"source":"Crossref","is-referenced-by-count":2,"title":["A Rigidity Property of Complete Systems of Mutually Unbiased Bases"],"prefix":"10.1142","volume":"28","author":[{"given":"M\u00e1t\u00e9","family":"Matolcsi","sequence":"first","affiliation":[{"name":"Department of Analysis, Institute of Mathematics, Budapest University of Technology and Economics, Muegyetem rkp. 3., H\u20131111 Budapest, Hungary"},{"name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics, Hungarian Academy of Sciences, H\u20131053, Realtanoda u 13-15, Budapest, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mih\u00e1ly","family":"Weiner","sequence":"additional","affiliation":[{"name":"Department of Analysis, Institute of Mathematics, Budapest University of Technology and Economics, Muegyetem rkp. 3., H\u20131111 Budapest, Hungary"},{"name":"Hungary and MTA-BME Lend\u00fclet Quantum Information Theory Research Group, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2022,5,10]]},"reference":[{"key":"S1230161221500128BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-002-0980-7"},{"key":"S1230161221500128BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-89994-5_6"},{"key":"S1230161221500128BIB003","doi-asserted-by":"publisher","DOI":"10.1063\/1.2716990"},{"key":"S1230161221500128BIB004","first-page":"371","volume":"7","author":"Boykin P. 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