Quantum fingerprinting with a single particle

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. The interpretation of these results is discussed in detail, and a possible experimental realization is proposed.