Distributed construction of quantum fingerprints

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