General theory of quantum fingerprinting network

Abstract

The purpose of fingerprinting is to compare long messages with low communication complexity. Compared with its classical version, quantum fingerprinting can realize exponential reduction in communication complexity. Recently, multiparty quantum fingerprinting is studied to determine whether the messages from many parties are all the same. However, the complete relationships among them, including which ones are the same, are more general for future applications. Here, we propose the relationship state G to describe all possible relationships among N messages. Based on this, we provide a general quantum fingerprinting network and then take the four-party quantum fingerprinting protocol as an example for detailed analysis. We take the full parameter optimization for the quantum fingerprinting protocol through asymmetric channel. The method of encoding more than one bit on each coherent state is used to further improve the performance of our protocol. Compared with other protocols, our protocol provides more relationships among different parties with only linear increase in communication complexity.