Analysis of Faraday-Michelson quantum key distribution system with unbalanced attenuation

Quantum key distribution (QKD) is a major research topic because it provides unconditional security. Unfortunately, many imperfections remain in QKD's experimental realization. The Faraday-Michelson (FM) QKD system is proposed to eliminate these imperfections using polarization. However, the long arm's phase modulator (PM) has an unexpected insertion loss, meaning that the state sent is no longer perfect. In this letter, we propose an alternative FM-QKD system structure, and analyze the security and key generation rate in comparison with the original system via diffeerent analysis methods. We find an obvious key rate improvement when the PM insertion loss is not extremely small.