A versatile construction of Bell inequalities for the multipartite scenario

Abstract

Local measurements acting on entangled quantum states give rise to a rich correlation structure in the multipartite scenario. We introduce a versatile technique to build families of Bell inequalities witnessing different notions of multipartite nonlocality for any number of parties. The idea behind our method is simple: a known Bell inequality satisfying certain constraints, for example the Clauser-Horne-Shimony-Holt inequality, serves as the seed to build new families of inequalities for more parties. The constructed inequalities have a clear operational meaning, capturing an essential feature of multipartite correlations: their violation implies that numerous subgroups of parties violate the inequality chosen as seed. The more multipartite nonlocal the correlations, the more subgroups can violate the seed. We illustrate our construction using different seeds and designing Bell inequalities to detect k-way nonlocal multipartite correlations, in particular, genuine multipartite nonlocal correlations-the strongest notion of multipartite nonlocality. For one of our inequalities we prove analytically that a large class of pure states that are genuine multipartite entangled (GME) exhibit genuine multipartite nonlocality for any number of parties, even for some states that are almost product. We also provide numerical evidence that this family is violated by all GME pure states of three and four qubits. Our results make us conjecture that this family of Bell inequalities can be used to prove the equivalence between genuine multipartite pure-state entanglement and nonlocality for any number of parties.

Genuine Multipartite Nonlocality Is Intrinsic to Quantum Networks

“…To prove the first case, we take bipartite inequalities between A 1 and each other party, lift them to three parties, and combine them using Refs. [55,60], to obtain the following GMNL inequality:…”

Tight Upper Bound for the Maximal Expectation Value of the N$N$‐Partite Generalized Svetlichny Operator

“…Multipartite Bell-type inequalities are an effective approach to describe multipartite correlations and provide insight into the rich structure of multipartite scenarios and thus much effort has been devoted to this research with a desire to gain a better understanding of GMNL. [17,[21][22][23] Furthermore, the significant advantage of GMNL lies in certifying the presence of genuine multipartite entanglement in a device-independent way by observing the violation of some genuine multipartite Bell-type inequalities. For progress in the experimental aspects of multipartite entanglement, see refs.…”

Unbounded Bell violations for quantum genuine multipartite non-locality

“…A natural way to get rid of these problems is to consider bilocal models in which correlations among subsets of parties are required to be non-signalling (see e.g. [2,13]). We will refer to these models as non-signalling bilocal.…”