  We propose that measurements of time-of-arrival correlations in multi-partite
systems can sharply distinguish between different approaches to the
time-of-arrival problem. To show this, we construct a Positive-Operator-Valued
measure for two distinct time-of-arrival measurements in a bipartite system,
and we prove that the resulting probabilities differ strongly from ones defined
in terms of probability currents. We also prove that time-of-arrival
correlations are entanglement witnesses, a result suggesting the use of
temporal observables for quantum information processing tasks. Finally, we
construct the probabilities for sequential time-of-arrival measurements on a
single particle. We derive the state-reduction rule for time-of-arrival
measurements; it differs significantly from the standard one, because
time-of-arrival measurements are not defined at a single predetermined moment
of time.
