  The standard Bell inequality experiments test for violation of local realism
by repeatedly making local measurements on individual copies of an entangled
quantum state. Here we investigate the possibility of increasing the violation
of a Bell inequality by making collective measurements. We show that
nonlocality of bipartite pure entangled states, quantified by their maximal
violation of the Bell-Clauser-Horne inequality, can always be enhanced by
collective measurements, even without communication between the parties. For
mixed states we also show that collective measurements can increase the
violation of Bell inequalities, although numerical evidence suggests that the
phenomenon is not common as it is for pure states.
