New Class of 4-Dim Kochen-Specker Sets

TL;DR

This paper introduces a new, highly symmetrical class of 4-dimensional Kochen-Specker vector sets, generated from a single initial set using a novel stripping technique, expanding the known configurations in quantum contextuality.

Contribution

The authors develop a new method to generate a vast class of 4D Kochen-Specker sets with unique symmetries, not derivable from previous sets, using a novel stripping technique.

Findings

Generated millions of non-isomorphic 4D KS sets

Identified geometrical properties of critical KS subsets

Presented algorithms for set generation

Abstract

We find a new highly symmetrical and very numerous class (millions of non-isomorphic sets) of 4-dim Kochen-Specker (KS) vector sets. Due to the nature of their geometrical symmetries, they cannot be obtained from previously known ones. We generate the sets from a single set of 60 orthogonal spin vectors and 75 of their tetrads (which we obtained from the 600-cell) by means of our newly developed "stripping technique." We also consider "critical KS subsets" and analyze their geometry. The algorithms and programs for the generation of our KS sets are presented.