Measuring Bell non-locality in the presence of signalling

Abstract Scientific inquiry seeks causal explanations of observed phenomena. The Bell experiment provides a paradigmatic case, revealing correlations between spatially separated systems that no local model can reproduce. Such correlations, known as Bell non-locality, are typically analyzed under the non-signalling assumption, which requires that local statistics be independent of distant measurement choices. Yet real experiments, as well as applications beyond physics, often involve signalling, raising the question of how non-locality should be characterized without this constraint. We introduce a general method for quantifying Bell non-locality in the presence of signalling, designed to relax locality as little as necessary. Our approach is guided by the question: how often can locality be preserved across repeated trials in explaining the observed correlations? The task reduces to finding the optimal convex decomposition of the observed correlations into local and non-local components. We solve this problem within the linear-programming framework, obtaining a closed-form solution valid for arbitrary correlations. We further evaluate a corresponding measure of signalling, demonstrating the generality of the method and the non-trivial character of the results. By extending the analysis of non-locality outside the non-signalling regime, our framework broadens the scope of experimental analysis both within and beyond physics, offering tools for settings where signaling and non-local contributions are difficult to disentangle.