Quantum key distribution with realistic heralded single photon sources
  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. 
Mikolaj Lasota, Rafal Demkowicz-Dobrzanski, Konrad Banaszek
quant-ph