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.

Highlights

  • The application of quantum mechanics in the field of communication brings benefits in many aspects, such as security and communication complexity

  • We propose the relationship state G to describe all possible relationships among N messages

  • In terms of communication complexity [8,9], which is the minimum amount of communication required among participants to complete a certain task, compared with its classical version [10,11], quantum fingerprinting can exponentially reduce the amount of information required for the tasks

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Summary

INTRODUCTION

The application of quantum mechanics in the field of communication brings benefits in many aspects, such as security and communication complexity. In terms of communication complexity [8,9], which is the minimum amount of communication required among participants to complete a certain task, compared with its classical version [10,11], quantum fingerprinting can exponentially reduce the amount of information required for the tasks. This is very useful in energy-saving communication [8,12,13].

Relationship state
Protocol
The design of N-party quantum fingerprinting network based on balanced BSs
Communication complexity
Relationship state G for four messages
Numerical results
Two-party quantum fingerprinting protocol through asymmetric channel
Fingerprinting network through asymmetric channel
DISCUSSION
CONCLUSION
Four-party quantum fingerprinting protocol through asymmetric channel

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