A two-parameter family of complex Hadamard matrices of order $6$ induced by hypocycloids
Open Access
- 1 March 2010
- journal article
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 138 (03) , 921
- https://doi.org/10.1090/s0002-9939-09-10102-8
Abstract
We construct a -parameter family of complex Hadamard matrices of order by a natural block construction. We combine this family with an earlier result of Zauner to derive a -parameter family of triplets of mutually unbiased bases (MUBs) in <!-- MATH $\mathbb{C}^6$ --> . This invalidates some numerical evidence given by Brierley and Weigert and sheds new light on the problem of determining the maximal number of MUBs in <!-- MATH $\mathbb{C}^6$ --> .
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