General theory of quantum fingerprinting network

The purpose of fingerprinting is to compare long messages with low communication complexity. Compared its classical version, the quantum can realize exponential reduction in Recently, multi-party studied on whether from many parties are same. However, sometimes it not enough just know these same, we usually need relationship among them. We provide a general model network, defining function $f^R$ and giving corresponding decision rules. In this work, take four-party protocol as an example for detailed analysis. also choose optimal parameters minimize complexity case asymmetric channels. Furthermore, based two-party find that has obvious advantages, especially terms time. Finally, method encoding more than one bit each coherent state used further improve performance protocol.