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

Metod Saniga; Michel Planat; Petr Pracna; Peter Levay

hal-00708602, version 1

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

Metod Saniga (, ) ¹, Michel Planat ², Petr Pracna ³, Peter Levay ⁴

Symmetry, Integrability and Geometry : Methods and Applications 8 (2012) 083

Résumé : 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.

1 : Astronomical Institute, Slovak Academy of Sciences (ASTRINSTSAV)
Astronomical Institute, Slovak Academy of Sciences
2 : Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (FEMTO-ST)
CNRS : UMR6174 – Université de Franche-Comté – Université de Technologie de Belfort-Montbeliard – Ecole Nationale Supérieure de Mécanique et des Microtechniques
3 : J. Heyrovsky institute of Physical Chemistry
J. Heyrovsky Institute of Physical Chemistry
4 : Budapest University of Technology and Economics (BME)
Budapest University of Technology and Economics

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Contributeur : Metod Saniga <>
Soumis le : Vendredi 15 Juin 2012, 14:13:01
Dernière modification le : Samedi 17 Novembre 2012, 11:37:54

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DOI : 10.3842/SIGMA.2012.083

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