Hypergraph Contextuality

TL;DR

This paper introduces a new hypergraph-based class of quantum contextual sets for qutrits, expanding the understanding of quantum contextuality and enabling simpler experimental implementations and new entropic contextualities.

Contribution

It presents a novel hypergraph-based framework for quantum contextual sets, complementing existing classes and providing practical, minimal sets for experimental testing.

Findings

Thousands of 3-dimensional contextual sets identified

Simplest sets involve only 5 observables, facilitating experiments

New entropic contextualities established

Abstract

Quantum contextuality is a source of quantum computational power and a theoretical delimiter between classical and quantum structures. It has been substantiated by numerous experiments and prompted generation of state independent contextual sets, that is, sets of quantum observables capable of revealing quantum contextuality for any quantum state of a given dimension. There are two major classes of state-independent contextual sets - the Kochen-Specker ones and the operator-based ones. In this paper, we present a third, hypergraph-based class of contextual sets. Hypergraph inequalities serve as a measure of contextuality. We limit ourselves to qutrits and obtain thousands of 3-dim contextual sets. The simplest of them involves only 5 quantum observables, thus enabling a straightforward implementation. They also enable establishing new entropic contextualities.