A Hierarchy of Multipartite Nonlocality and Device-Independent Effect Witnesses

TL;DR

This paper explores the hierarchy of multipartite nonlocality in quantum networks, revealing behaviors that distinguish different levels of nonlocality and their implications for device-independent certification of entangled measurements.

Contribution

It categorizes the hierarchy of GMNL definitions in three-party quantum networks and demonstrates behaviors that challenge existing notions of entangled measurements.

Findings

Existence of a behavior witnessing the most general GMNL in a simple scenario

Behavior can be simulated with bipartite states and entangled measurements

Some behaviors can be simulated with superquantum resources, challenging current theories

Abstract

According to recent new definitions, a multi-party behavior is genuinely multipartite nonlocal (GMNL) if it cannot be modeled by measurements on an underlying network of bipartite-only nonlocal resources, possibly supplemented with local (classical) resources shared by all parties. The new definitions differ on whether to allow entangled measurements upon, and/or superquantum behaviors among, the underlying bipartite resources. Here, we categorize the full hierarchy of these new candidate definitions of GMNL in three-party quantum networks, highlighting the intimate link to device-independent witnesses of network effects. A key finding is the existence of a behavior in the simplest nontrivial multi-partite measurement scenario (3 parties, 2 measurement settings, and 2 outcomes) that cannot be simulated in a bipartite network prohibiting entangled measurements and superquantum resources -- thus witnessing the most general form of GMNL -- but can be simulated with bipartite-only quantum states with an entangled measurement, indicating an approach to device independent certification of entangled measurements with fewer settings than in previous protocols. Surprisingly, we also find that this (3,2,2) behavior, as well as the others previously studied as device-independent witnesses of entangled measurements, can all be simulated at a higher echelon of the GMNL hierarchy that allows superquantum bipartite resources while still prohibiting entangled measurements. This poses a challenge to a theory-independent understanding of entangled measurements as an observable phenomenon distinct from bipartite nonlocality.