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

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 $\sqrt{g^{(3)}}+3\sqrt{g^{(2)}}\ge 2$. 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.

References in corpus (28)

• Quantum information with continuous variables
• Gaussian Quantum Information
• Interfacing single photons and single quantum dots with photonic nanostructures
• Quantum computation over continuous variables
• Squeezing as an irreducible resource
• Efficient Classical Simulation of Continuous Variable Quantum Information Processes
• A No-Go Theorem for Gaussian Quantum Error Correction
• Non-Gaussian Quantum States and Where to Find Them
• Observation of three-photon bound states in a quantum nonlinear medium
• Motional Fock states for quantum-enhanced amplitude and phase measurements with trapped ions
• Optimal state estimation for cavity optomechanical systems
• QuantumCumulants.jl: A Julia framework for generalized mean-field equations in open quantum systems
• Metrological Nonlinear Squeezing Parameter
• Experimental test of quantum non-Gaussianity of heralded single photon state
• Measuring photon anti-bunching from continuous variable sideband squeezing
• Faithful hierarchy of genuine $n$-photon quantum non-Gaussian light
• Certification of non-Gaussian states with operational measurements
• Quantum Non-Gaussian Multiphoton Light
• Squeezing and entanglement of density oscillations in a Bose-Einstein condensate
• Observation of three-body correlations for photons coupled to a Rydberg superatom
• Prediction and retrodiction with continuously monitored Gaussian states
• Quantum non-Gaussianity of light and atoms
• Unique Steady-State Squeezing in a Driven Quantum Rabi Model
• Quantum non-Gaussian Photon Coincidences
• Hierarchical Verification of Non-Gaussian Coherence in Bosonic Quantum States
• Coherence-based operational nonclassicality criteria
• Photon-number moments and cumulants of Gaussian states
• Quantum non-Gaussian high Fock states of light pulses and their superpositions