David Schmid - The interplay of entanglement and nonlocality demystified

Scheduled talk:
The interplay of entanglement and nonlocality demystified:
developing a new branch of entanglement theory

Abstract:
A standard approach to quantifying resources is to determine which operations on the resources are freely available and to deduce the partial order over resources that is 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, i.e., entanglement, then the common assumption is 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 the entanglement of states and the nonlocality of the correlations in a Bell experiment (the properties describing Bell inequality violations) are merely an artifact of the use of LOCC-entanglement and that if one uses LOSR-entanglement instead, then this interplay becomes natural and intuitive. Specifically, we show that the LOSR paradigm (i) provides a resolution of the anomaly of nonlocality, wherein partially entangled states exhibit more nonlocality than maximally entangled states, (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. Along the way, we derive some fundamental results concerning the necessary and sufficient conditions for convertibility between pure entangled states under LOSR and highlight some of their consequences, such as the impossibility of catalysis for bipartite pure states. Our results motivate the study of LOSR-entanglement as a new branch of entanglement theory.