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A two-parameter family of complex Hadamard matrices of order $ 6$ induced by hypocycloids


Author: Ferenc Szöllosi
Journal: Proc. Amer. Math. Soc. 138 (2010), 921-928
MSC (2000): Primary 46L10; Secondary 05B20
DOI: https://doi.org/10.1090/S0002-9939-09-10102-8
Published electronically: October 20, 2009
MathSciNet review: 2566558
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Abstract: We construct a $ 2$-parameter family of complex Hadamard matrices of order $ 6$ by a natural block construction. We combine this family with an earlier result of Zauner to derive a $ 2$-parameter family of triplets of mutually unbiased bases (MUBs) in $ \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 $ \mathbb{C}^6$.


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Additional Information

Ferenc Szöllosi
Affiliation: Institute of Mathematics and Its Applications, Central European University (CEU), H-1051, Nádor u. 9, Budapest, Hungary
Email: szoferi@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-09-10102-8
Received by editor(s): April 3, 2009
Published electronically: October 20, 2009
Additional Notes: This work was supported by Hungarian National Research Fund OTKA-K77748
Communicated by: Marius Junge
Article copyright: © Copyright 2009 American Mathematical Society

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