Systems of mutually unbiased Hadamard matrices containing real and complex matrices

摘要

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 cannot contain more than one real Hadamard matrix. We also give new proofs of several known structural results in low dimensions.