A characterization of complex Hadamard matrices appearing in families of MUB triplets
arXiv:2405.09991 · doi:10.1007/s10623-024-01503-w
Abstract
It is shown that a normalized complex Hadamard matrix of order having three distinct columns, each containing at least one entry necessarily belongs to the transposed Fourier family, or to the family of -circulant complex Hadamard matrices. The proofs rely on solving polynomial system of equations by Gröbner 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 .
17 pages, preprint