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

• URL: http://arxiv.org/abs/2202.08197v4
• Date: Mon, 9 Jan 2023 23:24:36 GMT
• Title: Automated Generation of Arbitrarily Many Kochen-Specker and Other Contextual Sets in Odd Dimensional Hilbert Spaces
• Authors: Mladen Pavicic and Norman. D. Megill
• Abstract summary: We give three methods for automated generation of arbitrarily many contextual KS and non-KS sets in any dimension. No explicit vectors for the original Kochen-Specker set were known so far, while we now generate them from 24 vector components.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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