Operational nonlocality

Abstract: An operational concept of locality whose quantum violation is indicated independently of any other assumption(s) seems to be lacking in the quantum foundations literature so far. Bell's theorem only shows that quantum correlations violate the conjunction of the ontological assumptions of localism and determinism. Taking a cue from computational complexity theory, here we define such a concept of locality in terms of a class of operational decision problems, and propose that Einstein-Podolsky-Rosen (EPR) steering in its basic asymmetric formulation gives a specific realization of this class. Various nonclassical (convex) operational theories, including quantum mechanics, are shown to be nonlocal according to this operational criterion. We discuss several ramifications arising from this result. It indicates a basic difference between quantum no-signaling and relativistic no-signaling, and suggests an information theoretic derivation of the former from other basic principles in the convex framework. It elucidates the connection between two different bounds on nonlocality, due to Oppenheim and Wehner (2010) and Banik et al. (2015), thereby highlighting the interplay and contrast between uncertainty and measurement incompatibility. Our result provides an argument supporting the realist interpretation of the quantum state, and helps clarify why Spekkens' toy model (2007) features steering but not Bell nonlocality.