Causal hierarchy of multipartite Bell nonlocality

TL;DR

This paper introduces a Bayesian network framework to classify and analyze all forms of multipartite Bell nonlocality, revealing new highly nonlocal structures and establishing the strongest known quantum nonlocality forms.

Contribution

It provides a comprehensive classification of multipartite Bell nonlocality using Bayesian networks, including the discovery of new nonlocal causal structures and a Bell-type inequality with no quantum violation.

Findings

Fully characterized all nonlocality classes in tripartite scenarios

Identified new highly nonlocal causal structures beyond quantum correlations

Derived a Bell-type inequality with no quantum violation

Abstract

As with entanglement, different forms of Bell nonlocality arise in the multipartite scenario. These can be defined in terms of relaxations of the causal assumptions in local hidden-variable theories. However, a characterisation of all the forms of multipartite nonlocality has until now been out of reach, mainly due to the complexity of generic multipartite causal models. Here, we employ the formalism of Bayesian networks to reveal connections among different causal structures that make a both practical and physically meaningful classification possible. Our framework holds for arbitrarily many parties. We apply it to study the tripartite scenario in detail, where we fully characterize all the nonlocality classes. Remarkably, we identify new highly nonlocal causal structures that cannot reproduce all quantum correlations. This shows, to our knowledge, the strongest form of quantum multipartite nonlocality known to date. Finally, as a by-product result, we derive a non-trivial Bell-type inequality with no quantum violation. Our findings constitute a significant step forward in the understanding of multipartite Bell nonlocality and open several venues for future research.