  Since Bell's theorem, it is known that quantum correlations cannot be
described by local variables (LV) alone: if one does not want to abandon
classical mechanisms for correlations, a superluminal form of communication
among the particles must be postulated. A natural question is whether such a
postulate would imply the possibility of superluminal signaling. Here we show
that the assumption of finite-speed superluminal communication indeed leads to
signaling when no LV are present, and more generally when only LV derivable
from quantum statistics are allowed. When the most general LV are allowed, we
prove in a specific case that the model can be made again consistent with
relativity, but the question remains open in general.
