Title




Saturated KochenSpeckertype configuration of 120 projective lines in eightdimensional space and its group of symmetry
 
Author




 
Abstract




There exists an example of a set of 40 projective lines in eightdimensional Hilbert space producing a KochenSpeckertype contradiction. This set corresponds to a known nohidden variables argument due to Mermin. In the present paper it is proved that this set admits a finite saturation, i.e., an extension up to a finite set with the following property: every subset of pairwise orthogonal projective lines has a completion, i.e., is contained in at least one subset of eight pairwise orthogonal projective lines. An explicit description of such an extension consisting of 120 projective lines is given. The idea to saturate the set of projective lines related to Mermin's example together with the possibility to have a finite saturation allow to find the corresponding group of symmetry. This group is described explicitely and is shown to be generated by reflections. The natural action of the mentioned group on the set of all subsets of pairwise orthogonal projective lines of the mentioned extension is investigated. In particular, the restriction of this action to complete subsets is shown to have only four orbits, which have a natural characterization in terms of the construction of the saturation. (C) 2005 American Institute of Physics. 
 
Language




English
 
Source (journal)




Journal of mathematical physics.  New York, N.Y.
 
Publication




New York, N.Y.
:
2005
 
ISSN




00222488
 
DOI




10.1063/1.1887923
 
Volume/pages




46
:5
(2005)
, p. 128
 
Article Reference




052109
 
ISI




000229155700009
 
Medium




Eonly publicatie
 
Full text (Publisher's DOI)




 
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