  As shown in the famous \emph{EPR} paper (Einstein, Podolsky e Rosen,1935),
Quantum Mechanics is non-local. The Bell theorem and the experiments by Aspect
and many others, ruled out the possibility of explaining quantum correlations
between entangled particles using local hidden variables models (except for
implausible combinations of loopholes). Some authors (Bell, Eberhard, Bohm and
Hiley) suggested that quantum correlations could be due to superluminal
communications (tachyons) that propagate isotropically with velocity
\emph{$v_{t}>c$} in a preferred reference frame. For finite values of
\emph{$v_{t}$}, Quantum Mechanics and superluminal models lead to different
predictions. Some years ago a Geneva group and our group did experiments on
entangled photons to evidence possible discrepancies between experimental
results and quantum predictions. Since no discrepancy was found, these
experiments established only lower bounds for the possible tachyon velocities
\emph{$v_{t}$}. Here we propose an improved experiment that should lead us to
explore a much larger range of possible tachyon velocities \emph{$v_{t}$} for
any possible direction of velocity $\vec{V}$ of the tachyons preferred frame.
