  Bipartite Bell inequalities can be simultaneously violated by two different
pairs of observers when weak measurements and signaling is employed. Here we
experimentally demonstrate the violation of two simultaneous CHSH inequalities
by exploiting a two-photon polarization maximally entangled state. Our results
demonstrate that large double violation is experimentally achievable. Our
demonstration may have impact for Quantum Key Distribution or certification of
Quantum Random Number generators based on weak measurements.
