In quantum information theory, the presence of Bell non-local correlations is a key indicator of non-classical behavior in multipartite quantum systems. However, non-locality is not exclusive to...Show moreIn quantum information theory, the presence of Bell non-local correlations is a key indicator of non-classical behavior in multipartite quantum systems. However, non-locality is not exclusive to quantum mechanics; more general theories with stronger non-local correlations than those achievable within the quantum formalism can be constructed. While distinguishing classical (local) correlations from non-local correlations can, in principle, be accomplished by a finite number of linear constraints called Bell inequalities, distinguishing between quantum and post-quantum correlations requires solving a hierarchy of SDP relaxations. To simplify the certification of quantum correlations, a whole line of research has focused on searching for an operational principle that can explain the limited strength of quantum correlations. Among the proposed principles, information causality (IC) stands out as the most promising, though deriving general correlation bounds from it is also very complex. We review the various attempts to formalise IC and their effectiveness in constraining bipartite non-locality, as well as the challenges encountered in studying this principle. In particular, we perform numerical experiments to showcase the insufficiency of all the currently proposed IC bounds to capture the full potential of the principle for correlations near the quantum boundary. Furthermore, we demonstrate the instability of two out of three bounds under non-locality distillation.Show less
