  We analyze theoretically performance of four-state quantum key distribution
protocols implemented with a realistic heralded single-photon source. The
analysis assumes a noisy model for the detector heralding generation of
individual photons via spontaneous parametric down-conversion, including dark
counts and imperfect photon number resolution. We identify characteristics of
the heralding detector that defines the attainable cryptographic key rate and
the maximum secure distance. Approximate analytical formulas are applied to
multiplexed detection and compared with results of numerical calculations.
