engleski

Parity proofs of the Bell-Kochen-Specker theorem based on the 600-cell

The set of 60 real rays in four dimensions derived from the vertices of a 600-cell is shown to possess numerous subsets of rays and bases that provide parity proofs of the Bell-Kochen- Specker (BKS) theorem. The subsets vary considerably in size and composition, with the smallest having 26 rays and 13 bases and the largest having 60 rays and 41 bases. There are at least 90 basic types of subsets, with many of them coming in a number of geometrically distinct varieties. The replicas of all the varieties under the symmetries of the 600- cell yield a total of almost a hundred million parity proofs of the BKS theorem. The proofs are all very transparent and take no more than simple counting to verify. A few proofs are exhibited, both in tabular form as well as in the form of MMP hypergraphs that assist in their visualization. A survey of the proofs is given, simple procedures for generating some of them are described, and their applications are discussed. It is shown that all four-dimensional parity proofs of the BKS theorem can be turned into experimental disproofs of noncontextuality.

Kochen-Specker theorem; MMP hypergraphs; critical Kochen-Specker sets

nije evidentirano