Entropic Test of Quantum Contextuality

TL;DR

This paper investigates quantum contextuality in three-level systems using classical entropy measures, deriving an inequality that non-contextual theories must satisfy, and identifies optimal measurements to experimentally test quantum contextuality.

Contribution

It introduces an entropic inequality for quantum contextuality, constructs minimal measurement configurations, and demonstrates the approach's extendability to higher dimensions.

Findings

Derived an entropic contextual inequality analogous to Bell inequalities.

Identified optimal measurements for violation of the inequality.

Approach is experimentally verifiable with current technology.

Abstract

We study the contextuality of a three-level quantum system using classical conditional entropy of measurement outcomes. First, we analytically construct the minimal configuration of measurements required to reveal contextuality. Next, an entropic contextual inequality is formulated, analogous to the entropic Bell inequalities derived by Braunstein and Caves in [Phys. Rev. Lett. {\bf 61}, 662 (1988)], that must be satisfied by all non-contextual theories. We find optimal measurements for violation of this inequality. The approach is easily extendable to higher dimensional quantum systems and more measurements. Our theoretical findings can be verified in the laboratory with current technology.