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.

References in corpus (3)

• Hidden Variables and the Two Theorems of John Bell
• Finite-precision measurement does not nullify the Kochen-Specker theorem
• Recursive proof of the Bell-Kochen-Specker theorem in any dimension $n>3$

Cited by in corpus (1)

• New Examples of Kochen-Specker Type Configurations on Three Qubits