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.

Figure 1

Quantum fingerprinting using a single photon with many internal degrees of freedom encoded in time bins. The mode-locked laser (M L Laser) produces a train of pulses which is coupled into an optical fiber. An attenuator (A) decreases the intensity so that the train contains less than a single photon. A coupler (C) sends with amplitude $1∕\sqrt{2}$ the train to Alice and with amplitude $1∕\sqrt{2}$ the train to Bob. Alice and Bob put phases on the successive pulses using their phase modulators ${\varphi }_A$ and ${\varphi }_B$. The pulses are then sent back to the referee who makes them interfere. If the phases ${\varphi }_A$ and ${\varphi }_B$ are equal, the photon exits by the equal port. If they are opposite, it exits by the not equal port. The photon is detected by single-photon detectors (D).