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

## TL;DR

This paper analyzes how dark counts affect single photon heralding using quasi-number-resolving detection, providing formulas for heralding probability, state fidelity, and optimal detection modes considering efficiency and dark count effects.

## Contribution

It introduces a formalism with closed-form expressions to evaluate the impact of dark counts on heralding performance and determines the optimal number of detection modes for given parameters.

## Key findings

- Dark counts limit the maximum number of detection modes for optimal heralding.
- Fidelity of the heralded state is maximized by balancing detection efficiency and dark count probability.
- Closed-form formulas enable precise assessment of heralding schemes under realistic conditions.

## Abstract

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, on the basis of optimizing this fidelity, due to the presence of dark counts there is a maximum number of detection modes worth multiplexing for each combination of efficiency and dark count probability.