  We show that the two slit experiment in which a single quantum particle
interferes with itself can be interpreted as a quantum fingerprinting protocol:
the interference pattern exhibited by the particle contains information about
the environment it encountered in the slits which would require much more
communication to learn classically than is required quantum mechanically. An
extension to the case where the particle has many internal degrees of freedom
is suggested and its interpretation is discussed in detail. A possible
experimental realization is proposed.
