A Quantum Non-Gaussianity Criterion Based on Photon Correlations $g^{(2)}$ and $g^{(3)}$

TL;DR

This paper introduces a new criterion based on photon correlations to identify quantum non-Gaussian states, demonstrating its effectiveness through experimental validation with a quantum dot single-photon source.

Contribution

It proposes an attenuation-resistant inequality involving $g^{(2)}$ and $g^{(3)}$ to confirm quantum non-Gaussianity, and experimentally verifies it with high statistical significance.

Findings

The criterion successfully detects quantum non-Gaussian states.

Experimental results show violation of the classical bound with high significance.

The method is robust against attenuation effects.

Abstract

Quantum non-Gaussian states, which cannot be written as mixtures of Gaussian states, are necessary to achieve a quantum advantage in continuous variable systems. They represent an important benchmark for the realization of an advanced quantum light source, as they cannot be made by simple means such as displacement and squeezing. We introduce an attenuation-resistant sufficient criterion for quantum non-Gaussian states based on the second- and third-order correlation functions, $g^{(2)}$ and $g^{(3)}$. The general non-linear bound for classical mixtures of Gaussian states is $\sqrt{g^{(3)}} + 3 \sqrt{g^{(2)}} \geq 2$. Any mixture of Gaussian states must fulfill this inequality, thus, the violation of it represents a direct confirmation of quantum non-Gaussianity. We experimentally show the non-Gaussianity of the state produced by a quantum dot single-photon source, where we obtain $\sqrt{g^{(3)}} + 3 \sqrt{g^{(2)}} = 0.174 (13)$, which represents a statistical significance of more than $100$ standard deviations.