A Hierarchy of Multipartite Nonlocality and Device-Independent Effect Witnesses

• URL: http://arxiv.org/abs/2301.12081v2
• Date: Tue, 4 Jul 2023 05:34:32 GMT
• Title: A Hierarchy of Multipartite Nonlocality and Device-Independent Effect Witnesses
• Authors: Peter Bierhorst, Jitendra Prakash
• Abstract summary: A multi-party behavior is genuinely multipartite nonlocal if it cannot be modeled by measurements on an underlying network of bipartite-only nonlocal resources. Here, we study the full hierarchy of these new candidate definitions of GMNL in three-party quantum networks. Surprisingly, we find that this 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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