# Photon-number parity of heralded single photons from a Bragg-reflection waveguide reconstructed loss-tolerantly via moment generating function

## TL;DR

This paper demonstrates a loss-tolerant method to measure the photon-number parity of heralded single photons generated in a semiconductor waveguide, using moment generating functions to overcome optical losses.

## Contribution

It introduces a novel loss-tolerant approach to determine photon-number parity via moment generating functions in heralded single-photon states.

## Key findings

- Photon-number parity can be reconstructed loss-tolerantly.
- The method effectively characterizes the photon-number content of heralded states.
- Experimental validation with a semiconductor waveguide and transition-edge sensors.

## Abstract

Due to their strict photon-number correlation, the twin beams produced in parametric down-conversion (PDC) work well for heralded state generation. Often, however, this state manipulation is distorted by the optical losses in the herald and by the higher photon-number contributions inevitable in the PDC process. In order to find feasible figures of merit for characterizing the heralded states, we investigate their normalized factorial moments of the photon number that can be accessed regardless of the optical losses in the detection. We then perform a measurement of the joint photon statistics of twin beams from a semiconductor Bragg-reflection waveguide with transition-edge sensors acting as photon-number-resolving detectors. We extract the photon-number parity of heralded single photons in a loss-tolerant fashion by utilizing the moment generating function. The photon-number parity is highly practicable in quantum state characterization, since it takes into account the complete photon-number content of the target state.