The faraday mirror (FM) plays a very important role in maintaining thestability of two way plug-and-play quantum key distribution (QKD) system.However, the practical FM is imperfect, which will not only introduceadditional quantum bit error rate (QBER) but also leave a loophole for Eve tospy the secret key. In this paper, we propose a passive faraday mirror attackin 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 fourstates sent by Alice is three instead of two. Thus Eve can distinguish thesestates with a set of POVM operators belonging to three dimension space, whichwill reduce the QBER induced by her attack. Furthermore, a relationship betweenthe degree of the imperfection of FM and the transmittance of the practical QKDsystem is obtained. The results show that, the probability that Eve loads herattack successfully depends on the degree of the imperfection of FM rapidly,but the QBER induced by Eve's attack changes with the degree of theimperfection of FM slightly.
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