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arXiv · 2405.09991

A characterization of complex Hadamard matrices appearing in families of MUB triplets

Ákos K. Matszangosz·Ferenc Szöllősi
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Abstract

It is shown that a normalized complex Hadamard matrix of order $6$ having three distinct columns, each containing at least one $-1$ entry necessarily belongs to the transposed Fourier family, or to the family of $2$-circulant complex Hadamard matrices. The proofs rely on solving polynomial system of equations by Gr\"obner basis techniques, and make use of a structure theorem concerning regular Hadamard matrices. As a consequence, members of these two families can be easily recognized in practice. In particular, one can identify complex Hadamard matrices appearing in known triplets of pairwise mutually unbiased bases in dimension $6$.

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Ákos K. Matszangosz, Ferenc Szöllősi. 2024-05-16. A characterization of complex Hadamard matrices appearing in families of MUB triplets. https://doi.org/10.1007/s10623-024-01503-w

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