Bell-type Inequalities for Arbitrary Non-Cyclic Networks

TL;DR

This paper develops a method to construct Bell-type inequalities for any tree-structured network, enabling the analysis of quantum correlations beyond standard Bell scenarios, and demonstrates their violation by quantum theory.

Contribution

It introduces an iterative procedure to generate Bell inequalities for arbitrary tree networks, extending the scope of Bell tests beyond cyclic configurations.

Findings

Strong quantum violations of the derived inequalities

Applicability to various tree-structured networks

Extension of Bell inequality framework

Abstract

Bell inequalities bound the strength of classical correlations between observers measuring on a shared physical system. However, studies of physical correlations can be considered beyond the standard Bell scenario by networks of observers sharing some configuration of many independent physical systems. Here, we show how to construct Bell-type inequalities for correlations arising in any tree-structured network i.e. networks without cycles. This is achieved by an iteration procedure that in each step allows one to add a branch to the tree-structured network and construct a corresponding Bell-type inequality. We explore our inequalities in several examples, in all of which we demonstrate strong violations from quantum theory.