Classical and quantum fingerprinting with shared randomness and   one-sided error
  Within the simultaneous message passing model of communication complexity, under a public-coin assumption, we derive the minimum achievable worst-case error probability of a classical fingerprinting protocol with one-sided error. We then present entanglement-assisted quantum fingerprinting protocols attaining worst-case error probabilities that breach this bound. 
Rolf T. Horn, A. J. Scott, Jonathan Walgate, Richard Cleve, A. I.   Lvovsky and Barry C. Sanders