General theory of quantum fingerprinting network

TL;DR

This paper introduces a comprehensive quantum fingerprinting network model that assesses relationships among multiple messages, optimizing communication efficiency and demonstrating advantages over two-party protocols through detailed analysis and encoding improvements.

Contribution

It presents a general model for multi-party quantum fingerprinting, analyzes a four-party protocol, and enhances performance by encoding multiple bits per coherent state.

Findings

Multi-party quantum fingerprinting reduces communication time compared to two-party protocols.

Optimal parameters minimize communication complexity in asymmetric channels.

Encoding multiple bits per coherent state further improves protocol performance.

Abstract

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 quantum 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.