Passive faraday mirror attack in practical two-way quantum key distribution system

TL;DR

This paper reveals how imperfections in Faraday mirrors in two-way quantum key distribution systems can be exploited by an eavesdropper to distinguish quantum states more effectively, potentially compromising security.

Contribution

It introduces a passive attack method exploiting FM imperfections, analyzing its impact on QKD security and the relationship between FM imperfection and system transmittance.

Findings

Eve can distinguish states with a three-dimensional POVM due to FM imperfection.

The attack success probability increases rapidly with FM imperfection.

QBER changes slightly with FM imperfection, affecting security analysis.

Abstract

The faraday mirror (FM) plays a very important role in maintaining the stability of two way plug-and-play quantum key distribution (QKD) system. However, the practical FM is imperfect, which will not only introduce additional quantum bit error rate (QBER) but also leave a loophole for Eve to spy the secret key. In this paper, we propose a passive faraday mirror attack in two way QKD system based on the imperfection of FM. Our analysis shows that, if the FM is imperfect, the dimension of Hilbert space spanned by the four states sent by Alice is three instead of two. Thus Eve can distinguish these states with a set of POVM operators belonging to three dimension space, which will reduce the QBER induced by her attack. Furthermore, a relationship between the degree of the imperfection of FM and the transmittance of the practical QKD system is obtained. The results show that, the probability that Eve loads her attack successfully depends on the degree of the imperfection of FM rapidly, but the QBER induced by Eve's attack changes with the degree of the imperfection of FM slightly.