Quantum violation of entropic non-contextual inequality in four-dimension

TL;DR

This paper introduces an entropic inequality for four-level quantum systems based on Shannon entropy, which is satisfied by non-contextual hidden variable models but violated by quantum mechanics, including entangled and product states, and can be experimentally tested.

Contribution

The paper proposes a new entropic inequality for four-dimensional systems that distinguishes quantum mechanics from non-contextual hidden variable models.

Findings

Quantum mechanics violates the entropic inequality for certain states.

The inequality applies to both entangled and product states.

Experimental testing of the inequality is feasible with current technology.

Abstract

Using joint Shannon entropy, we propose an inequality for a four-level system, which is satisfied in any non-contextual realist hidden variable model. We show that this entropic inequality is violated by quantum mechanics for a range of entangled, as well as product states. Our inequality can be experimentally tested using the existing technology.