Monogamy relations for relativistically causal correlations

Non-signalling conditions encode minimal requirements that any (quantum) systems put into spatial arrangements must satisfy in order to be consistent with special relativity. Recent works have argued that in scenarios involving more that two parties, conditions compatible with relativistic causality do not have to satisfy all possible non-signalling conditions but only a subset of them. Here we show that correlations satisfying only this subset of constraints have to satisfy highly non-local monogamy relations between the effects of space-like separated random variables. These monogamy relations take the form of new entropic inequalities between the various systems and we give a general method to derive them. Using these monogamy relations we refute previous suggestions for physical mechanisms that could lead to relativistically causal correlations, demonstrating that such mechanisms would lead to superluminal signalling.