Proposal of a two-qutrit contextuality test free of the finite precision and compatibility loopholes

TL;DR

This paper proposes a new two-qutrit contextuality test that overcomes finite precision and compatibility loopholes by ensuring measurements are performed on separated qutrits, enabling more reliable experimental verification of quantum contextuality.

Contribution

It introduces a novel set of inequalities for two-qutrit systems that guarantee measurement compatibility through spatial separation, independent of Kochen-Specker constructions.

Findings

Demonstrates violations of noncontextual inequalities with separated qutrits

Addresses finite precision and compatibility loopholes in contextuality tests

Provides a practical framework for experimental tests of quantum contextuality

Abstract

It has been argued that any test of quantum contextuality is nullified by the fact that perfect orthogonality and perfect compatibility cannot be achieved in finite precision experiments. We introduce experimentally testable two-qutrit violations of inequalities for noncontextual theories in which compatibility is guaranteed by the fact that measurements are performed on separated qutrits. The inequalities are inspired by the basic building block of the Kochen-Specker proof of quantum contextuality for a qutrit, despite the fact that their proof is completely independent of it.