Non-bicolourable Finite Configurations of Rays and Their Deformations

Details Non-bicolourable Finite Configurations of Rays and Their Deformations Non-bicolourable Finite Configurations of Rays and Their Deformations

2009-06-15

arxiv.org/abs/0906.2693v1

J. Phys. A 39 (2006), no. 10, 2457--2476

Physics

Quantum Physics

Scientific paper

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.

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