Quantum non-locality based on finite-speed causal influences leads to superluminal signalling

The experimental violation of Bell inequalities using space-like separated measurements precludes the explanation of quantum correlations through causal influences propagating at subluminal speed^{1, 2}. Yet, any such experimental violation could always be explained in principle through models based on hidden influences propagating at a finite speed v>c, provided v is large enough^{3, 4}. Here, we show that for any finite speed v with , such models predict correlations that can be exploited for faster-than-light communication. This superluminal communication does not require access to any hidden physical quantities, but only the manipulation of measurement devices at the level of our present-day description of quantum experiments.