  In this paper, we introduce a "coherence equality" that is satisfied by any
classical communication -- i.e., conveyed by a localized carrier traveling
along well defined directions. In contrast, this equality is violated when the
carrier is prepared in a quantum superposition of communication directions.
This is phrased in terms of the success probability of a certain communication
task, which results to be always constant and equal to 1/2 in the classical
case. On the other hand, we develop two simple quantum schemes that deviate
systematically from the classical value, thus violating the coherence equality.
Such a violation can also be exploited as an operational way to witness spatial
quantum superpositions without requiring the use of an interferometer, but only
by means of spatially separated local measurements.
