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 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.

V2 changes: Accepted by Quantum, bibliography hyperlinks adjusted according to journal policy. New narrative in the introduction

References in corpus (8)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
• Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
• Quantum Mechanics as Quantum Information (and only a little more)
• Sum-of-squares decompositions for a family of CHSH-like inequalities and their application to self-testing
• Non-locality distillation and post-quantum theories with trivial communication complexity
• Nonlocality free wirings and the distinguishability between Bell boxes
• Channel Steering

Cited by in corpus (10)

• The resource theory of nonclassicality of channel assemblages
• A Compendious Review of Majorization-Based Resource Theories: Quantum Information and Quantum Thermodynamics
• Every non-signalling channel is common-cause realizable
• Activation of post-quantumness in bipartite generalised EPR scenarios
• Certifying nonlocal properties of noisy quantum operations
• Localization of joint quantum measurements on ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$ by entangled resources with Schmidt number at most $d$
• Activation of post-quantum steering
• Quantum Assemblage Tomography
• No-local-broadcasting theorem for non-signalling behaviours and assemblages
• Operational Coherent Measurements with Steering and Randomness