  Although quantum key distribution (QKD) is theoretically secure, there is a
gap between the theory and practice. In fact, real-life QKD may not be secure
because component devices in QKD systems may deviate from the theoretical
models assumed in security proofs. To solve this problem, it is necessary to
construct the security proof under realistic assumptions on the source and
measurement unit. In this paper, we prove the security of a QKD protocol under
practical assumptions on the source that accommodate fluctuation of the phase
and intensity modulations. As long as our assumptions hold, it does not matter
at all how the phase and intensity distribute nor whether or not their
distributions over different pulses are independently and identically
distributed (I.I.D.). Our work shows that practical sources can be safely
employed in QKD experiments.
