  Quantum fingerprints are useful quantum encodings introduced by Buhrman,
Cleve, Watrous, and de Wolf (Physical Review Letters, Volume 87, Number 16,
Article 167902, 2001; quant-ph/0102001) in obtaining an efficient quantum
communication protocol. We design a protocol for constructing the fingerprint
in a distributed scenario. As an application, this protocol gives rise to a
communication protocol more efficient than the best known classical protocol
for a communication problem.
