We expand the toolbox for studying Bell correlations in multipartite systems by introducing permutationally invariant Bell inequalities (PIBIs) involving few-body correlators. First, we present around twenty families of PIBIs with up to three- or four-body correlators, that are valid for arbitrary number of particles. Compared to known inequalities, these show higher noise robustenss, or the capability to detect Bell correlations in highly non-Gaussian spin states. We then focus on finding PIBIs that are of practical experimental implementation, in the sense that the associated operators require collective spin measurements along only a few directions. To this end, we formulate this search problem as a semidefinite program that embeds the constraints required to look for PIBIs of the desired form.
@article{arxiv.2303.13499,
title = {Detecting Bell correlations in multipartite non-Gaussian spin states},
author = {Jiajie Guo and Jordi Tura and Qiongyi He and Matteo Fadel},
journal= {arXiv preprint arXiv:2303.13499},
year = {2023}
}