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

Abstract : In this paper we exhibit the existence of an {\it infinite family of triplets} of mutually unbiased bases (MUBs) in dimension 6. These triplets involve the Fourier family of Hadamard matrices, $F(a,b)$. The emergence of such an infinite family is surprising because only a handful of isolated examples of MUB-triplets have been known in the literature so far. However, we also prove that {\it no triplet of the infinite family can be extended to a MUB-quartet}. We consider this latter result a breakthrough in that the {\it method} of proof may successfully be applied in the future to prove that the maximal number of MUBs in dimension 6 is three.
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Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2009, 42 (24), pp.245305. 〈10.1088/1751-8113/42/24/245305〉
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https://hal.archives-ouvertes.fr/hal-00359160
Contributeur : Philippe Jaming <>
Soumis le : vendredi 6 février 2009 - 10:33:25
Dernière modification le : jeudi 3 mai 2018 - 15:32:06

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P. Jaming, M. Matolcsi, P. Móra, F. Szöllösi, M. Weiner. A generalized Pauli problem and an infinite family of MUB-triplets in dimension 6. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2009, 42 (24), pp.245305. 〈10.1088/1751-8113/42/24/245305〉. 〈hal-00359160〉

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