  Quantum theory is inconsistent with any local hidden variable model as was
first shown by Bell. To test Bell inequalities two separated observers extract
correlations from a common ensemble of identical systems. Since quantum theory
does not allow simultaneous measurements of noncommuting observables, on each
system every party measures a single randomly chosen observable out of a given
set. Here we suggest a different approach for testing Bell inequalities that is
experimentally realizable by current methods. We show that Bell inequalities
can be maximally violated even when all observables are measured on each member
of the ensemble. This is possible by using weak measurements that produce small
disturbance, at the expense of accuracy. However, our approach does not
constitute an independent test of quantum nonlocality since the local hidden
variables may correlate the noise of the measurement instruments. Nevertheless,
by adding a randomly chosen precise measurement at the end of every cycle of
weak measurements, the parties can verify that the hidden variables were not
interfering with the noise, and thus validate the suggested test.
