Real and complex unbiased Hadamard matrices

Details Real and complex unbiased Hadamard matrices Real and complex unbiased Hadamard matrices

2012-01-03

arxiv.org/abs/1201.0631v1

Mathematics

Combinatorics

13 pages

Scientific paper

We use combinatorial and Fourier analytic arguments to prove various non-existence results on systems of real and complex unbiased Hadamard matrices. In particular, we prove that a complete system of complex mutually unbiased Hadamard matrices (MUHs) in any dimension $d$ cannot contain more than one real Hadamard matrix. We also give new proofs of several known structural results in low dimensions, for $d\le 6$.

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