Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces

Abstract

Development of quantum computation and communication, recently shown to be supported by contextuality, arguably asks for a requisite supply of contextual sets. While that has been achieved in even dimensional spaces, in odd dimensional spaces only a dozen contextual critical Kochen-Specker (KS) sets have been found so far. In this paper we give three methods for automated generation of arbitrarily many contextual KS and non-KS sets in any dimension for possible future application and implementation and we employ them to obtain millions of KS and other contextual sets in dimensions 3, 5, 7, and 9 where previously only a handful of sets have been found. Also, no explicit vectors for the original Kochen-Specker set were known so far, while we now generate them from 24 vector components.