Role of non-classicality in mediated spatial quantum correlations

TL;DR

This paper introduces a new inequality linking quantum correlations between probes to the non-commutativity of a mediator's observables, providing a framework to witness non-classicality across quantum-to-classical transitions.

Contribution

It proposes a quantitative inequality connecting quantum correlations to mediator non-commutativity and tests it across different degrees of non-classicality, including classical limits.

Findings

The inequality effectively captures the quantum-to-classical transition.

Simulations show the reduction of non-commutativity correlates with decreased quantum correlations.

The framework is independent of specific interaction dynamics.

Abstract

The study of non-classicality is essential to understand the quantum-to-classical transition in physical systems. Recently, a witness of non-classicality has been proposed, linking the ability of a system (``the mediator") to create quantum correlations between two quantum probes with its non-classicality, intended as the existence of at least two non-commuting variables. Here, we propose a new inequality that quantitatively links the increase in quantum correlations between the probes to a function of the non-commutativity of the mediator's observables. We test the inequality for various degrees of non-classicality of the mediator, from fully quantum to fully classical. This quantum-to-classical transition is simulated via a phase-flip channel applied to the mediator, inducing an effective reduction of the non-commutativity of its variables. Our results provide a general framework for witnessing non-classicality, assessing the non-classicality of a system via its intrinsic properties, independently of the specific chosen interaction dynamics.