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arXiv · 0902.0882

A generalized Pauli problem and an infinite family of MUB-triplets in dimension 6

P. Jaming·M. Matolcsi·P. Móra·F. Szöllősi·M. Weiner
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Abstract

We exhibit an infinite family of {\it 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 $F(a,b)$ {\it cannot be extended to a MUB-quartet}. The main novelty lies in the {\it 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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P. Jaming, M. Matolcsi, P. Móra, F. Szöllősi, M. Weiner. 2009-02-26. A generalized Pauli problem and an infinite family of MUB-triplets in dimension 6. https://doi.org/10.1088/1751-8113%2F42%2F24%2F245305

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