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Bell scenarios involve space-like separated measurements made by multipleparties. The standard no-signalling constraints ensure that such parties cannotsignal superluminally by choosing their measurement settings. In tripartiteBell scenarios, relaxed non-signalling constraints have been proposed, whichpermit a class of post-quantum theories known as jamming non-local theories. Toanalyse whether no superluminal signalling continues to hold in these theoriesand, more generally, the role of non-signalling constraints in preservingrelativistic causality principles, we apply a framework that we have recentlydeveloped for defining information-theoretic causal models in non-classicaltheories and their compatibility with relativistic causality in a space-time.We show that any theory that generates jamming correlations in a Bell scenariobetween space-like separated parties must necessarily do so through causalfine-tuning and by means of superluminal causal influences. Moreover, withinour framework, we show that jamming theories can also lead to superluminalsignalling (contrary to previous claims) unless it is ensured that certainsystems are fundamentally inaccessible to agents and their interventions.Finally, we analyse relativistic causality in Bell scenarios showing thatno-signalling constraints on correlations are generally insufficient for rulingout superluminal signalling when general interventions are also allowed. Inthis way, we identify necessary and sufficient conditions for ruling outsuperluminal signalling in Bell scenarios, and demonstrate through examplesthat the non-signalling constraints on correlations are neither necessary norsufficient for ruling out causal loops. These results solidify ourunderstanding of relativistic causality principles in information processingtasks in space-time, involving classical, quantum or post-quantum resources.

A causal modelling analysis of Bell scenarios in space-time: implications of jamming non-local correlations for relativistic causality principles