Quantum fingerprinting without a shared phase reference

We discuss quantum fingerprinting in a scenario when the parties preparing optical signals that carry data fingerprints do not share a phase reference. We show that a protocol based on two-photon interference in principle provides scaling analogous to the recently proposed and demonstrated scheme using coherent pulses and first-order interference. The effects of signal attenuation can be mitigated by resorting to higher-order optical interference and using joint photon number statistics at the interferometer output for statistical inference.