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

The development of quantum computation and communication, recently shown to be supported by contextu-ality, 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 Letter, we give three methods for the 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, we generate explicit vectors for the original Kochen-Specker set from 24 vector components.

Automated summary

The development of quantum computation and communication requires a large supply of contextual sets. This study presents three methods for the automated generation of contextual sets in any dimension and successfully generates millions of new contextual sets in odd dimensions.