### 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 this 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.

Original language | English |
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Article number | 245305 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 42 |

Issue number | 24 |

DOIs | |

Publication status | Published - Nov 23 2009 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

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## Cite this

Jaming, P., Matolcsi, M., Móra, P., Szöllosi, F., & Weiner, M. (2009). A generalized Pauli problem and an infinite family of MUB-triplets in dimension 6.

*Journal of Physics A: Mathematical and Theoretical*,*42*(24), [245305]. https://doi.org/10.1088/1751-8113/42/24/245305