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

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 -endorsed by EPR themselves -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.

On characterising assemblages in Einstein-Podolsky-Rosen scenarios

“…For a deeper discussion on the advantages of taking this less-common inferential perspective we refer the reader to Ref. [63].…”

On characterising assemblages in Einstein–Podolsky–Rosen scenarios

“…Notice that this discourse is different from the ubiquitous one where EPR scenarios are about non-classical causal influences, the famous 'spooky action at a distance'. For a deeper discussion on the advantages of taking this less-common inferential perspective we refer the reader to reference [63]. Bipartite EPR scenario: Alice refines her knowledge about the state of Bob's quantum system by making inferences from performing measurements on her share of the system.…”

Assemblages and steering in general probabilistic theories

“…The steering degree of assemblages of shape k can be quantified by the amount of noise that needs to be mixed with the assemblage {ρ a|x } in order to obtain a classical assemblage, this is also called steering robustness [27]. The noise is represented by assemblages of the same shape k. Steering robustness is a monotone in various resource theories of steering, [14] or [37]. See [10,11] for some variants, as well as some other possibilities of quantifying steering in (quantum) assemblages.…”