English

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

Quantum Physics 2023-01-11 v4 Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.2202.08197,
  title  = {Automated Generation of Arbitrarily Many Kochen-Specker and Other Contextual Sets in Odd Dimensional Hilbert Spaces},
  author = {Mladen Pavicic and Norman. D. Megill},
  journal= {arXiv preprint arXiv:2202.08197},
  year   = {2023}
}

Comments

32 pages, 7 figures, 1 table; submitted to Phys. Rev. Lett., Quantum Journal, Phys. Rev A (accepted); referee's reports and responses to them enclosed