Logical and inequality based contextuality for qudits

TL;DR

This paper generalizes logical and inequality-based contextuality proofs for qudits of any dimension greater than three, showing constant quantum violations and addressing experimental imprecision.

Contribution

It introduces a new approach using compatibility graphs specific to qudits, extending previous contextuality proofs to higher dimensions.

Findings

Constructs states and measurements satisfying the compatibility graphs.

Demonstrates logical and inequality-based contextuality for qudits.

Shows quantum violation remains constant as dimension increases.

Abstract

In this work we present a generalization of the recently developed Hardy-like logical proof of contextuality and of the so-called KCBS contextuality inequality for any qudit of dimension greater than three. Our approach uses compatibility graphs that can only be satisfied by qudits. We find a construction for states and measurements that satisfy these graphs and demonstrate both logical and inequality based contextuality for qudits. Interestingly, the quantum violation of the inequality is constant as dimension increases. We also discuss the issue of imprecision in experimental implementations of contextuality tests and a way of addressing this problem using the notion of ontological faithfulness.