Why standard entanglement theory is inappropriate for the study of Bell scenarios

A standard approach to quantifying resources is to determine which operations are freely available and to deduce the partial order over resources induced by the relation of convertibility under the free operations. If the resource of interest is the nonclassicality of the correlations embodied in a quantum state, that is, entanglement, then it is a near-universal presumption that the appropriate choice of free operations is Local Operations and Classical Communication (LOCC). We here argue that this is not the best choice for quantifying entanglement in one of the most prominent applications of entanglement theory, namely, the study of Bell scenarios. A better choice, we claim, is Local Operations and Shared Randomness (LOSR). We support this thesis by showing that various perverse features of the interplay between entanglement and nonlocality are resolved in the LOSR paradigm. Specifically, focussing on LOSR (i) provides a resolution of the anomaly of nonlocality, (ii) entails a notion of genuine multipartite entanglement that is distinct from the conventional one and which is free of several of its pathological features, and (iii) makes possible a resource-theoretic account of the self-testing of entangled states which simplifies and generalizes prior results.