Bipartite non-locality beyond Bell inequalities by means of multivariable correlations
Abstract
We give a set of necessary conditions for locality in bipartite systems, which include and generalize known Bell's inequalities. Each condition corresponds to a specific order of the expansion of random variables defined on graphs, in terms of genuinely n-variable correlation functions. The first non-trivial order leads to known Bell inequalities, while higher orders produce additional, non-equivalent conditions. In particular, in CHSH settings, we obtain at least two additional tight conditions which do not reduce to the CHSH inequality. This shows that tight Bell inequalities are sufficient but not necessary conditions for the non-locality of bipartite quantum correlations.
Keywords
Cite
@article{arxiv.2004.12968,
title = {Bipartite non-locality beyond Bell inequalities by means of multivariable correlations},
author = {Bruno Leggio and Bruno Bellomo and Romain Azaïs and Przemysław Prusinkiewicz and Christophe Godin},
journal= {arXiv preprint arXiv:2004.12968},
year = {2020}
}
Comments
We withdraw the version v1 of this manuscript. Due to a flaw in our interpretation of part of the work of which we have been made aware, our claim that inequalities of order > 2 are needed to detect non-locality in CHSH settings is no longer substantiated by results. The rest of the work, notably the method to obtain Bell inequalities from equalities of path variables, still stands