Security of practical phase-coding quantum key distribution

Security proof of practical quantum key distribution (QKD) has attracted a lot of atten-tions in recent years. Most of real-life QKD implementations are based on phase-codingBB84 protocol, which usually use Unbalanced Mach-Zehnder Interferometer (UMZI) asthe information encoder and decoder. However, the long arm and short arm of UMZIwill introduce different loss in practical experimental realizations, the state emitted byAlice's side is nolonger perfect BB84 states correspondingly. In this paper, we will givethe security analysis in this situation. Counterintuitively, active compensation for thisdifferent loss will only lower the secret key bit rate.

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