Automated Generation of Arbitrarily Many Kochen-Specker and Other Contextual Sets in Odd Dimensional Hilbert Spaces

TL;DR

This paper introduces three automated methods to generate vast numbers of Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces, significantly expanding the known sets and providing explicit vectors for the original KS set.

Contribution

It presents new algorithms for generating many contextual sets in any dimension, including explicit vectors for the original KS set, advancing the study of quantum contextuality.

Findings

Generated millions of KS and contextual sets in dimensions 3, 5, 7, and 9.

Provided explicit vectors for the original Kochen-Specker set.

Enabled future applications in quantum computation and communication.

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.