A resource theory of nonclassicality in Bell scenarios

Abstract

We take a resource-theoretic approach to the problem of quantifying nonclassicality in Bell scenarios. The resources are conceptualized as probabilistic processes from the setting variables to the outcome variables which have a particular causal structure, namely, one wherein the wings are only connected by a common cause. The distinction between classical and nonclassical is then defined in terms of whether or not a classical causal model can explain the correlations. The relative nonclassicality of such resources is quantified by considering their interconvertibility relative to the set of operations that can be implemented using a classical common cause (which correspond to local operations and shared randomness). Among other results, we show that the information contained in the degrees of violation of facet-defining Bell inequalities is not sufficient for quantifying nonclassicality, even though it is sufficient for witnessing nonclassicality. In addition to providing new insights on Bell nonclassicality, our work sets the stage for quantifying nonclassicality in more general causal networks and thus also for a resource-theoretic account of nonclassicality in computational settings. (Joint work with Elie Wolfe, David Schmid, Ana Belen Sainz, and Ravi Kunjwal)