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.

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

References in corpus (5)

• Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality
• Vector Generation of Quantum Contextual Sets in Even Dimensional Hilbert Spaces
• Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets
• Automated generation of Kochen-Specker sets
• Hypergraph Contextuality

Cited by in corpus (4)

• Quantum Contextuality
• Non-Kochen-Specker Contextuality
• Quantum Contextual Hypergraphs, Operators, Inequalities, and Applications in Higher Dimensions
• Generation of Kochen-Specker contextual sets in higher dimensions by dimensional upscaling whose complexity does not scale with dimension and their applications