Non-bicolourable Finite Configurations of Rays and Their Deformations

Abstract

A new infinite family of examples of finite non-bicolorable configurations of rays in Hilbert space is described. Such configurations appear in the analysis of quantum mechanics in terms of Bell's inequalities and Kochen-Specker theorem and illustrate that there is no measurable space in the background of the probability model of a quantum system. The mentioned examples are naturally parametrized by a positive integer divisible by four and by several complex-valued parameters, whose number depends on this integer. In order to compare two configurations with the same number of rays, a notion of deformation of a configuration is introduced. The constructed examples are then interpreted as obtained by way of deformations.