### 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 |
---|---|

Article number | 245305 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 42 |

Issue number | 24 |

DOIs | |

Publication status | Published - 2009 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*42*(24), [245305]. https://doi.org/10.1088/1751-8113/42/24/245305

**A generalized Pauli problem and an infinite family of MUB-triplets in dimension 6.** / Jaming, Philippe; Matolcsi, M.; Móra, Péter; Szöllosi, Ferenc; Weiner, Mihály.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 42, no. 24, 245305. https://doi.org/10.1088/1751-8113/42/24/245305

}

TY - JOUR

T1 - A generalized Pauli problem and an infinite family of MUB-triplets in dimension 6

AU - Jaming, Philippe

AU - Matolcsi, M.

AU - Móra, Péter

AU - Szöllosi, Ferenc

AU - Weiner, Mihály

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=70449688158&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70449688158&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/42/24/245305

DO - 10.1088/1751-8113/42/24/245305

M3 - Article

VL - 42

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 24

M1 - 245305

ER -