Real and complex unbiased Hadamard matrices

Abstract

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 $d\le 6$.

13 pages

References in corpus (3)

• On mutually unbiased bases
• Maximal Sets of Mutually Unbiased Quantum States in Dimension Six
• Numerical evidence for the maximum number of mutually unbiased bases in dimension six

Cited by in corpus (2)

• On properties of Karlsson Hadamards and sets of Mutually Unbiased Bases in dimension six
• Almost Hadamard matrices: general theory and examples