Quantifying EPR: the resource theory of nonclassicality of common-cause assemblages

Einstein-Po dolsky-Rosen (EPR) steering is often (implicitly or explicitly) taken to be evidence for spooky action-at-a-distance. An alternative perspective on steer-ing is that Alice has no causal influence on the physical state of Bob???s system; rather, Alice merely updates her knowledge of the state of Bob???s system by performing a measurement on a system correlated with his. In this work, we elaborate on this per-spective (from which the very term ???steering??? is seen to be inappropriate), and we are led to a resource-theoretic treatment of correlations in EPR scenarios. For both bi-partite and multipartite scenarios, we develop the resulting resource theory, wherein the free operations are local operations and shared randomness (LOSR). We show that resource conversion under free operations in this paradigm can be evaluated with a single instance of a semidefinite program, making the problem numerically tractable. Moreover, we find that the structure of the pre-order of resources fea-tures interesting properties, such as infinite families of incomparable resources. In showing this, we derive new EPR resource monotones. We also discuss advantages of our approach over a pre-existing proposal for a resource theory of ???steering???, and discuss how our approach sheds light on basic questions, such as which multipartite assemblages are classically explainable.

Automated summary

Einstein-Podolsky-Rosen (EPR) steering can be explained by Alice updating her knowledge of Bob's system through measurements on a correlated system, rather than having a causal influence on Bob's system. We propose a resource-theoretic treatment of correlations in EPR scenarios, where local operations and shared randomness (LOSR) are considered as free operations. We show that resource conversion under free operations can be solved using a single instance of a semidefinite program, and we find interesting properties in the pre-order structure of resources.