Strength of statistical evidence for genuine tripartite nonlocality

Abstract: Recent advancements in network nonlocality have led to the concept of local operations and shared randomness-based genuine multipartite nonlocality (LOSR-GMNL). In this paper, we consider two recent experimental demonstrations of LOSR-GMNL, focusing on a tripartite scenario where the goal is to exhibit correlations impossible in a network where each two-party subset shares bipartite resources and every party has access to unlimited shared randomness. Traditional statistical analyses measuring violations of witnessing inequalities by the number of experimental standard deviations do not account for subtleties such as memory effects. We demonstrate a more sound method based on the prediction-based ratio (PBR) protocol to analyse finite experimental data and quantify the strength of evidence in favour of genuine tripartite nonlocality in terms of a valid $p$-value. In our work, we propose an efficient modification of the test factor optimisation using an approximating polytope approach. By justifying a further restriction to a smaller polytope we enhance practical feasibility while maintaining statistical rigour.