  A parametric down-conversion (PDC) source can be used as either a triggered
single photon source or an entangled photon source in quantum key distribution
(QKD). The triggering PDC QKD has already been studied in the literature. On
the other hand, a model and a post-processing protocol for the entanglement PDC
QKD are still missing. In this paper, we fill in this important gap by
proposing such a model and a post-processing protocol for the entanglement PDC
QKD. Although the PDC model is proposed to study the entanglement-based QKD, we
emphasize that our generic model may also be useful for other non-QKD
experiments involving a PDC source. Since an entangled PDC source is a basis
independent source, we apply Koashi-Preskill's security analysis to the
entanglement PDC QKD. We also investigate the entanglement PDC QKD with two-way
classical communications. We find that the recurrence scheme increases the key
rate and Gottesman-Lo protocol helps tolerate higher channel losses. By
simulating a recent 144km open-air PDC experiment, we compare three
implementations -- entanglement PDC QKD, triggering PDC QKD and coherent state
QKD. The simulation result suggests that the entanglement PDC QKD can tolerate
higher channel losses than the coherent state QKD. The coherent state QKD with
decoy states is able to achieve highest key rate in the low and medium-loss
regions. By applying Gottesman-Lo two-way post-processing protocol, the
entanglement PDC QKD can tolerate up to 70dB combined channel losses (35dB for
each channel) provided that the PDC source is placed in between Alice and Bob.
After considering statistical fluctuations, the PDC setup can tolerate up to
53dB channel losses.
