Non-bicolourable finite configurations of rays and their deformationsNon-bicolourable finite configurations of rays and their deformations
Faculty of Sciences. Mathematics and Computer Science

Fundamental Mathematics

article

2006London, 2006

Journal of physics: A: mathematical and general. - London, 1968 - 2006

39(2006):10, p. 2457-2476

0305-4470

000236776000015

E

English (eng)

A new infinite family of examples of finite non-bicolourable configurations of rays in Hilbert space is described. Such configurations appear in the analysis of quantum mechanics in terms of Bell's inequalities and the 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 4 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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