# Autocorrelation functions: a useful tool for both state and detector characterisation

## TL;DR

This paper demonstrates how autocorrelation functions, specifically the $g^{(2)}$ function, can be used to characterize quantum states of light and assess detector effects in mesoscopic multi-mode twin-beam states.

## Contribution

It introduces a method to evaluate the $g^{(2)}$ autocorrelation function for detected photons to analyze quantum state properties and detector imperfections.

## Key findings

- Autocorrelation functions effectively characterize quantum states of light.
- The $g^{(2)}$ function reveals statistical properties of mesoscopic twin-beam states.
- Autocorrelation functions help estimate spurious effects in Silicon-photomultiplier detectors.

## Abstract

The calculation of autocorrelation functions represents a routinely used tool to characterise quantum states of light. In this paper, we evaluate the $g^{(2)}$ function for detected photons in the case of mesoscopic multi-mode twin-beam states in order to fully investigate their statistical properties starting from measurable quantities. Moreover, we show that the second-order autocorrelation function is also useful to estimate the spurious effects affecting the employed Silicon-photomultiplier detectors.