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The no-signaling constraints state that the probability distribution of theoutputs of any subset of parties is independent of the inputs of thecomplementary set; here we re-examine these to see how they arise fromrelativistic causality. We show that while the usual no-signaling constraintsare sufficient, in general they are not necessary to ensure that a theory doesnot violate causality. Depending on the exact space-time coordinates of themeasurement events in a multi-party Bell experiment, causality only imposes asubset of the usual no-signaling conditions. After revisiting the derivation ofthe two-party no-signaling constraints, we consider the three-party Bellscenario and characterise a space-time region in which a subset of theno-signaling conditions is sufficient to preserve causality. Secondly, weexamine the implications for device-independent cryptography against aneavesdropper constrained only by the laws of relativity. We show an explicitattack in certain measurement configurations on a family of protocols based onthe n-party Mermin inequalities that were previously proven secure under theold no-signaling conditions. We then show that security of two-party protocolscan also be compromised when the eavesdropper's measurement configuration isnot constrained. The monogamy of non-local correlations that underpin their usein secrecy can also be broken in certain space-time configurations. Thirdly, weinspect the notion of free-choice and propose a definition of free-choice inthe multi-party Bell experiment. We then re-examine the question whetherquantum correlations may admit explanations by finite speed superluminalinfluences. Finally, we study genuine multiparty non-locality and present a newclass of causal bilocal models. We propose a new Svetlichny-type inequalitythat is satisfied by the causal bilocal model and show its violation withinquantum theory.

Relativistic Causality vs. No-Signaling as the limiting paradigm for correlations in physical theories