{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T00:56:42Z","timestamp":1775091402972,"version":"3.50.1"},"reference-count":11,"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":[[2008,6]]},"abstract":"<jats:p> Complex Hadamard matrices have received considerable attention in the past few years due to their application in quantum information theory. While a complete characterization currently available [5] is only up to order 5, several new constructions of higher order matrices have appeared recently [4, 12, 2, 7, 11]. In particular, the classification of self-adjoint complex Hadamard matrices of order 6 was completed by Beuachamp and Nicoara in [2], providing a previously unknown non-affine one-parameter orbit. In this paper we classify all dephased, symmetric complex Hadamard matrices with real diagonal of order 6. Furthermore, relaxing the condition on the diagonal entries we obtain a new non-affine one-parameter orbit connecting the Fourier matrix F<jats:sub>6<\/jats:sub> and Di\u0163\u0103's matrix D<jats:sub>6<\/jats:sub>. This answers a recent question of Bengtsson et al. [3]. <\/jats:p>","DOI":"10.1142\/s1230161208000092","type":"journal-article","created":{"date-parts":[[2008,6,13]],"date-time":"2008-06-13T10:55:40Z","timestamp":1213354540000},"page":"93-108","source":"Crossref","is-referenced-by-count":23,"title":["Towards a Classification of 6 \u00d7 6 Complex Hadamard Matrices"],"prefix":"10.1142","volume":"15","author":[{"given":"M\u00e1t\u00e9","family":"Matolcsi","sequence":"first","affiliation":[{"name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics, Hungarian Academy of Sciences, POB 127, H\u20131364 Budapest, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ferenc","family":"Sz\u00f6ll\u0151si","sequence":"additional","affiliation":[{"name":"Budapest University of Technology and Economics (BUTE), H\u20131111, Egry J. u. 1, Budapest, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,1,25]]},"reference":[{"key":"rf1","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0101073","volume-title":"Hadamard Matrices and Their Applications","volume":"1168","author":"Agaian S. S.","year":"1985"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1063\/1.2716990"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/37\/20\/008"},{"key":"rf5","unstructured":"U.\u00a0Haagerup, Operator Algebras and Quantum Field Theory (Rome) (International Press, Cambridge, MA, 1996)\u00a0pp. 296\u2013322."},{"key":"rf6","first-page":"147","volume":"311","author":"de la Harpe P.","journal-title":"C. A. Acad. Sci. Paris, serie I"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/s11080-007-9050-6"},{"key":"rf8","first-page":"329","volume":"314","author":"Munemasa A.","journal-title":"C. R. Acad. Sci. Paris, serie I"},{"key":"rf9","first-page":"295","volume":"55","author":"Nicoara R.","journal-title":"J. Operator Theory"},{"key":"rf10","first-page":"253","volume":"9","author":"Popa S.","journal-title":"J. Operator Theory"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/s11080-006-8220-2"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/34\/35\/332"}],"container-title":["Open Systems &amp; Information Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1230161208000092","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T01:56:07Z","timestamp":1565142967000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1230161208000092"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,6]]},"references-count":11,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2012,1,25]]},"published-print":{"date-parts":[[2008,6]]}},"alternative-id":["10.1142\/S1230161208000092"],"URL":"https:\/\/doi.org\/10.1142\/s1230161208000092","relation":{},"ISSN":["1230-1612","1793-7191"],"issn-type":[{"value":"1230-1612","type":"print"},{"value":"1793-7191","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,6]]}}}