A generalized Pauli problem and an infinite family of MUB-triplets in dimension 6
Abstract
We exhibit an infinite family of triplets of mutually unbiased bases (MUBs) in dimension 6. These triplets involve the Fourier family of Hadamard matrices, F(a,b). However, in the main result of the paper we also prove that for any values of the parameters (a,b), the standard basis and F(a,b) cannot be extended to a MUB-quartet. The main novelty lies in the method of proof which may successfully be applied in the future to prove that the maximal number of MUBs in dimension 6 is three.
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