Non-Kochen-Specker Contextuality

TL;DR

This paper introduces general, scalable methods for generating non-Kochen-Specker hypergraphs in any dimension, expanding the understanding of quantum contextuality beyond traditional Kochen-Specker sets.

Contribution

It provides dimension-independent, probabilistic algorithms to generate non-Kochen-Specker hypergraphs, with examples up to 16 dimensions, advancing the study of quantum contextuality.

Findings

Generated non-Kochen-Specker hypergraphs in up to 16 dimensions.

Developed scalable, probabilistic methods for hypergraph generation.

Enabled filtering of hypergraphs based on size and structure.

Abstract

Quantum contextuality supports quantum computation and communication. One of its main vehicles is hypergraphs. The most elaborated are the Kochen-Specker ones, but there is also another class of contextual sets that are not of this kind. Their representation has been mostly operator-based and limited to special constructs in three- to six-dim spaces, a notable example of which is the Yu-Oh set. Previously, we showed that hypergraphs underlie all of them, and in this paper, we give general methods - whose complexity does not scale up with the dimension - for generating such non-Kochen-Specker hypergraphs in any dimension and give examples in up to 16-dim spaces. Our automated generation is probabilistic and random, but the statistics of accumulated data enable one to filter out sets with the required size and structure.