  Security proof of practical quantum key distribution (QKD) has attracted a
lot of attentions in recent years. Most of real-life QKD implementations are
based on phase-coding BB84 protocol, which usually uses Unbalanced Mach-Zehnder
Interferometer (UMZI) as the information coder and decoder. However, the long
arm and short arm of UMZI will introduce different loss in practical
experimental realizations, the state emitted by Alice's side is nolonger
standard BB84 states. In this paper, we will give a security analysis in this
situation. Counterintuitively, active compensation for this different loss will
only lower the secret key bit rate.
