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arxiv: 1201.0631 · v1 · pith:OD5ZCHFPnew · submitted 2012-01-03 · 🧮 math.CO

Real and complex unbiased Hadamard matrices

Mate Matolcsi , Imre Z. Ruzsa , Mihaly Weiner This is my paper
classification 🧮 math.CO
keywords hadamardcomplexmatricesrealunbiasedproveresultsanalytic
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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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  1. Mutually Unbiased Bases in Composite Dimensions -- A Review

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    This review compiles fourteen equivalent formulations of the open existence problem for maximal mutually unbiased bases in composite dimensions and summarizes known analytic, computer-aided and numerical results along...