# Causal hierarchy of multipartite Bell nonlocality

Rafael Chaves1,2, Daniel Cavalcanti3, and Leandro Aolita4

1International Institute of Physics, Federal University of Rio Grande do Norte, 59078-970, P. O. Box 1613, Natal, Brazil
2Institute for Theoretical Physics, University of Cologne, 50937 Cologne, Germany
3ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
4Instituto de F'isica, Universidade Federal do Rio de Janeiro, P. O. Box 68528, Rio de Janeiro, RJ 21941-972, Brazil

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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.

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[2] Martin Ringbauer, Rafael Chaves, "Probing the non-classicality of temporal correlations", Quantum 1, 35 (2017).

[3] Erika Bene, Tamás Vértesi, "Measurement incompatibility does not give rise to Bell violation in general", New Journal of Physics 20, 013021 (2018).

[4] Francesco Andreoli, Gonzalo Carvacho, Luca Santodonato, Rafael Chaves, Fabio Sciarrino, "Maximal qubit violation of n-locality inequalities in a star-shaped quantum network", New Journal of Physics 19, 113020 (2017).

[5] Paul Skrzypczyk, "Causality: relaxing before exploring", Quantum Views 1, 3 (2017).

[6] Nikolai Miklin, Alastair A Abbott, Cyril Branciard, Rafael Chaves, Costantino Budroni, "The entropic approach to causal correlations", New Journal of Physics 19, 113041 (2017).

[7] S. G. A. Brito, B. Amaral, R. Chaves, "Quantifying Bell nonlocality with the trace distance", Physical Review A 97, 022111 (2018).

(The above data is from Crossref's cited-by service. Unfortunately not all publishers provide suitable and complete citation data so that some citing works or bibliographic details may be missing.)