Title: Contextuality and Fano Pentads
Author: Metod Saniga
Abstract:
Given the symplectic polar space of type W(5,2), let us call a set of five Fano planes sharing
pairwise a single point a Fano pentad. Once 63 points of W(5,2) are appropriately labeled by
63 canonical three-qubit observables, any such Fano pentad gives rise to a quantum contextual
set known as a Mermin pentagram. It will be shown that a Fano pentad also hosts another, closely
related contextual set, which features 25 observables and 30 three-element contexts. Out of 25
observables, ten are such that each of them is on six contexts, while each of the remaining 15
observables belongs to two contexts only. The totality of 12,096 such contextual sets is seen to
comprise 47 distinct types, falling into eight families according to the number (3,5,7,...,17)
of negative contexts.