Role of nonclassicality in mediated spatial quantum correlations

The study of nonclassicality is essential to understand the quantum-to-classical transition in physical systems. Recently, a witness of nonclassicality has been proposed, linking the ability of a system (the mediator) to create quantum correlations between two quantum probes with its nonclassicality, intended as the existence of at least two noncommuting variables. Here we propose an inequality that quantitatively links the increase in quantum correlations between the probes to a function of the noncommutativity of the mediator's observables. We test the inequality for various degrees of nonclassicality 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 noncommutativity of its variables. Our results provide a general framework for witnessing nonclassicality, assessing the nonclassicality of a system via its intrinsic properties, independently of the specific chosen interaction dynamics.