Fig. 5: Log–log plot of the amount of communication between Alice/Bob and Charlie in different fingerprinting protocols, as a function of input size n.

The solid red curve represents the best-known classical fingerprinting protocol²⁵. The purple squares are the amount of communication in our demonstration of coherent quantum fingerprinting (CQF) with wavelength-division multiplexing (WDM). Six-wavelength channels are used. Except for the 6.9 km DCF, the overall distance between Alice and Bob is about 40 km. The orange circles correspond to the amount of communication in the original CQF system (k = 1) under the same experimental parameters. It is clear that less information is communicated in our experiment than that in both the classical fingerprinting and the original CQF protocol. We also plot out the amount of communication in another CQF experiment with a single-wavelength channel³⁰ (green diamonds) for further comparison. Ref. ³⁰ uses the same single-photon detectors as ours, but has a much shorter distance (only about 5 km). As shown, our WDM–CQF system outperforms the original CQF system.