### Abstract

Recently Waegell and Aravind [J. Phys. A: Math. Theor. 45 (2012), 405301, 13 pages] have given a number of distinct sets of three-qubit observables, each furni- shing a proof of the Kochen-Specker theorem. Here it is demonstrated that two of these sets/configurations, namely the 18_{2} - 12_{3} and 2_{4}14_{2} - 4_{3}6_{4} ones, can uniquely be extended into geometric hyperplanes of the split Cayley hexagon of order two, namely into those of types V_{22}(37; 0; 12; 15; 10) and V_{4}(49; 0; 0; 21; 28) in the classification of Frohardt and John- son [Comm. Algebra 22 (1994), 773-797]. Moreover, employing an automorphism of order seven of the hexagon, six more replicas of either of the two configurations are obtained.

Original language | English |
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Article number | 083 |

Journal | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) |

Volume | 8 |

DOIs | |

Publication status | Published - Nov 6 2012 |

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### Keywords

- 'Magic' configurations of observables
- Split cayley hexagon of order two
- Three-qubit pauli group

### ASJC Scopus subject areas

- Analysis
- Mathematical Physics
- Geometry and Topology