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

TL;DR

This paper develops a resource-theoretic framework for EPR correlations, enabling quantification and comparison of nonclassicality in quantum assemblages using semidefinite programming, revealing complex resource structures.

Contribution

It introduces a novel resource theory of EPR assemblages based on local operations and shared randomness, with new monotones and a tractable evaluation method.

Findings

Resource conversion evaluated via semidefinite programming

Discovery of infinite families of incomparable resources

New monotones for EPR resource quantification

Abstract

Einstein-Podolsky-Rosen (EPR) steering is often (implicitly or explicitly) taken to be evidence for spooky action-at-a-distance. An alternative perspective on steering 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 perspective (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 bipartite 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 features 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.