Effect of dark counts on single-photon heralding with quasi-number-resolving detection schemes

We consider photon heralding with quasi-number-resolving detection schemes and account for detection efficiencies and dark count probabilities. With a straightforward formalism, we develop closed-form expressions for the heralding probability, photon number distribution of the resulting heralded state, and fidelity of this heralded state to a single-photon state. We calculate that this fidelity has a maximum as a function of the number of multiplexed detection modes and that, for experimental configurations in which the maximum is reached for quite a large number of detection modes, it can still be highly beneficial to multiplex fewer modes.