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arXiv · 1209.4315

Unbiased complex Hadamard matrices and bases

Darcy Best·Hadi Kharaghani
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Abstract

We introduce mutually unbiased complex Hadamard (MUCH) matrices and show that the number of MUCH matrices of order 2n, n odd, is at most 2 and the bound is attained for n = 1,5,9. Furthermore, we prove that certain pairs of mutually unbiased complex Hadamard matrices of order m can be used to construct pairs of unbiased real Hadamard matrices of order 2m. As a consequence we generate a new pair of unbiased real Hadamard matrices of order 36.

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Darcy Best, Hadi Kharaghani. 2012-09-19. Unbiased complex Hadamard matrices and bases. https://arxiv.org/abs/1209.4315

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