'Magic' Configurations of Three-Qubit Observables and Geometric Hyperplanes of the Smallest Split Cayley Hexagon - Archive ouverte HAL Access content directly
Journal Articles Symmetry, Integrability and Geometry : Methods and Applications Year : 2012

'Magic' Configurations of Three-Qubit Observables and Geometric Hyperplanes of the Smallest Split Cayley Hexagon

Abstract

Recently (arXiv:1205.5015), Waegell and Aravind have given a number of distinct sets of three-qubit observables, each furnishing 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 ${\cal V}_{22}(37; 0, 12, 15, 10)$ and ${\cal V}_{4}(49; 0, 0, 21, 28)$ in the classification of Frohardt and Johnson (Communications in Algebra 22 (1994) 773). Moreover, employing an automorphism of order seven of the hexagon, six more replicas of either of the two configurations are obtained.
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Dates and versions

hal-00708602 , version 1 (15-06-2012)

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Metod Saniga, Michel Planat, Petr Pracna, Peter Levay. 'Magic' Configurations of Three-Qubit Observables and Geometric Hyperplanes of the Smallest Split Cayley Hexagon. Symmetry, Integrability and Geometry : Methods and Applications, 2012, 8, pp.083. ⟨10.3842/SIGMA.2012.083⟩. ⟨hal-00708602⟩
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