# Evaluating Performance of Photon-Number-Resolving Detectors

## TL;DR

This paper evaluates the accuracy of photon-number-resolving detectors using a new figure of merit, analyzing how quantum efficiency affects their photon resolution capabilities through simulations.

## Contribution

It introduces a figure of merit for PNR detector accuracy and derives the quantum efficiency needed for resolving different photon numbers.

## Key findings

- High quantum efficiency is necessary for moderate photon resolution.
- The required number of click detectors grows quadratically with the maximum photon number.
- Simulations demonstrate the performance limits of multiplexed PNR detectors.

## Abstract

We analyze the performance of photon-number-resolving (PNR) detectors and introduce a figure of merit for the accuracy of such detectors. This figure of merit is the (worst-case) probability that the photon-number-resolving detector correctly predicts the input photon number. Simulations of various PNR detectors based on multiplexed single-photon `click detectors' is performed. We conclude that the required quantum efficiency is very high in order to achieve even moderate (up to a handful) photon resolution, we derive the required quantum efficiency as a function of the the maximal photon number one wants to resolve, and we show that the number of click detectors required grows quadratically with the maximal number of photons resolvable.