The construction of Kochen-Specker noncolourable sets in higher-dimensional space from corresponding sets in lower dimension: modification of Cabello, Estebaranz and Garcia-Alcaine's method

摘要

By re-examination of Cabello, Estebaranz and Garcia-Alcaine's method (CEG) for constructing a ray set which gives a proof of Kochen-Specker theorem in a higher dimension from an already known set in a lower dimension, a more refined method is derived. In the construction of ray sets of higher dimension, we need fewer rays than in CEG. By using the method, an analytical proof of the KS-noncolourability of ray sets in real Hilbert spaces is also given whose KS-noncolourability was found by CEG by computer calculation.