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

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 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 ${\mathcal{V}}_{22}(37;0,12,15,10)$ and ${\mathcal{V}}_4(49;0,0,21,28)$ in the classification of Frohardt and Johnson [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.

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Cited by in corpus (3)

• Grassmannian Connection Between Three- and Four-Qubit Observables, Mermin's Contextuality and Black Holes
• Distinguished three-qubit 'magicity' via automorphisms of the split Cayley hexagon
• Hexagons govern three-qubit contextuality