14 research outputs found
'Magic' Configurations of Three-Qubit Observables and Geometric Hyperplanes of the Smallest Split Cayley Hexagon
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 and ones, can uniquely be extended into geometric hyperplanes of the
split Cayley hexagon of order two, namely into those of types and 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