The purpose of fingerprinting is to compare long messages with low communication complexity. Compared with its classical version, the quantum fingerprinting can realize exponential reduction in communication complexity. Recently, the multi-party quan
tum fingerprinting is studied on whether the messages from many parties are the same. However, sometimes it is not enough just to know whether these messages are the same, we usually need to know the relationship among them. We provide a general model of quantum fingerprinting network, defining the relationship function $f^R$ and giving the corresponding decision rules. In this work, we take the four-party quantum fingerprinting protocol as an example for detailed analysis. We also choose the optimal parameters to minimize communication complexity in the case of asymmetric channels. Furthermore, we compare the multi-party quantum fingerprinting with the protocol based on the two-party quantum fingerprinting and find that the multi-party protocol has obvious advantages, especially in terms of communication time. Finally, the method of encoding more than one bit on each coherent state is used to further improve the performance of the protocol.
On the basis of the existing trace distance result, we present a simple and efficient method to tighten the upper bound of the guessing probability. The guessing probability of the final key k can be upper bounded by the guessing probability of anoth
er key k, if k can be mapped from the final key k. Compared with the known methods, our result is more tightened by thousands of orders of magnitude. For example, given a 10^{-9}-secure key from the sifted key, the upper bound of the guessing probability obtained using our method is 2*10^(-3277). This value is smaller than the existing result 10^(-9) by more than 3000 orders of magnitude. Our result shows that from the perspective of guessing probability, the performance of the existing trace distance security is actually much better than what was assumed in the past.
