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arXiv:2511.08488 · Physical Review Letters

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

Christoph Hotter, Clara Henke, Cornelis Jacobus van Diepen, Peter Lodahl, Anders Søndberg Sørensen

quant-phSubmitted Nov 11, 2025• Announced Nov 12, 2025• 1 citation• Revised Jun 23, 2026 (v2)
v1 · Nov 11, 2025v2 · Jun 23, 2026
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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.

Journal reference
Phys. Rev. Lett. 136, 243601 (2026)
DOI
10.1103/1t2q-qm97

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A Quantum Non-Gaussianity Criterion Based on Photon Correlations g(2)g^{(2)}g(2) and g(3)g^{(3)}g(3)
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Abstract Quantum non-Gaussian states represent an important class of highly non-classical states whose preparation requires quantum operations or measurements beyond the class of Gaussian operations and statistical mixing. Here we derive criteria for certification of quantum non-Gaussianity based on probability of vacuum in the original quantum state and a state transmitted through a lossy channel with transmittance T . We prove that the criteria hold for arbitrary multimode states, which is important for their applicability in experiments with broadband sources and single-photon detectors. Interestingly, our approach allows to detect quantum non-Gaussianity using only one photodetector instead of complex multiplexed photon detection schemes, at the cost of increased experimental time. We also formulate a quantum non-Gaussianity criterion based on the vacuum probability and mean photon number of the state and we show that this criterion is closely related to the criteria based on pair of vacuum probabilities. We illustrate the performance of the obtained criteria on the example of realistic imperfect single-photon states modeled as a mixture of vacuum and single-photon states with background Poissonian noise.
Entanglement is central to quantum physics, yet detecting and exploiting it in non-Gaussian systems remains a major challenge. In continuous variable platforms, standard inseparability criteria based on Gaussian statistics-such as the Duan-Simon criterion-fail when quantum correlations are encoded in higher moments of the field quadratures. Here we introduce a framework for detecting non-Gaussian entanglement using higher-order quadrature cumulants. In the Gaussian limit, the lowest order condition reduces to the Duan criterion, while higher-order violations reveal entanglement inaccessible to second-order methods. We experimentally demonstrate a tomography-free certification of inseparability in photon-subtracted squeezed states of light, where Gaussian witnesses fail despite the presence of entanglement. We further show that such higher-order inseparability enables enhanced quantum teleportation of Wigner negativity as compared to Gaussian protocols. These results identify higher-order cumulants as natural observables for non-Gaussian entanglement and open new routes to harnessing non-Gaussian resources in continuous variable quantum technologies.
What g(2)(0)<1/2g^{(2)}(0)<1/2g(2)(0)<1/2 tells you - and what it does not
Quantum-optical research on semiconductor quantum dots puts special emphasis on the measurement of the second-order correlation function g(2)(τ)g^{(2)}(\tau)g(2)(τ), arguing that g(2)(0)<1/2g^{(2)}(0)<1/2g(2)(0)<1/2 implies the source field represents a good single-photon light source. We analyze this claim theoretically. A quantum state of light having no projection on the single-photon Fock state can not give a value of g(2)(0)<1/2g^{(2)}(0)<1/2g(2)(0)<1/2. However, with solely the value of g(2)(0)g^{(2)}(0)g(2)(0), the amplitude of this single-photon projection can be arbitrarily small, owing to vacuum contributions. Yet, one can determine a lower bound on the ratio of single-to-multi-photon emission from g(2)(0)g^{(2)}(0)g(2)(0). For a fixed ratio of single-to-multi-photon emission, g(2)(0)g^{(2)}(0)g(2)(0) is artificially enhanced by the vacuum contributions. We derive an effective second-order correlation function, which corrects this enhancement, substantially improving the lower bound. The results are applied to theoretical and realized experimental setups and indicate that the quality of solid-state single-photon sources, at least with respect to this criterion, is often underestimated.
The non-Gaussianity of quantum states incarnates an important resource for improving the performance of continuous-variable quantum information protocols. We propose a novel criterion of non-Gaussianity for single-mode rotationally symmetric quantum states via the squared Frobenius norm of higher-order cumulant matrix for the quadrature distribution function. As an application, we study the non-Gaussianities of three classes of single-mode symmetric non-Gaussian states: a mixture of vacuum and Fock states, single-photon added thermal states, and even/odd Schrödinger cat states. It is shown that such a criterion is faithful and effective for revealing non-Gaussianity. We further extend this criterion to two cases of symmetric multi-mode non-Gaussian states and non-symmetric single-mode non-Gaussian states.
Gaussian states have played an important role in the physics of continuous-variable quantum systems.They are appealing for the experimental ease with which they can be produced, and for their compact and elegant mathematical description.Nevertheless, many proposed quantum technologies require us to go beyond the realm of Gaussian states and introduce non-Gaussian elements.In this Tutorial, we provide a roadmap for the physics of non-Gaussian quantum states.We introduce the phase-space representations as a framework to describe the different properties of quantum states in continuous-variable systems.We then use this framework in various ways to explore the structure of the state space.We explain how non-Gaussian states can be characterized not only through the negative values of their Wigner function, but also via other properties such as quantum non-Gaussianity and the related stellar rank.For multimode systems, we are naturally confronted with the question of how non-Gaussian properties behave with respect to quantum correlations.To answer this question, we first show how non-Gaussian states can be created by performing measurements on a subset of modes in a Gaussian state.Then, we highlight that these measured modes must be correlated via specific quantum correlations to the remainder of the system to create quantum non-Gaussian or Wigner-negative states.On the other hand, non-Gaussian operations are also shown to enhance or even create quantum correlations.Finally, we demonstrate that Wigner negativity is a requirement to violate Bell inequalities and to achieve a quantum computational advantage.At the end of the Tutorial, we also provide an overview of several experimental realizations of non-Gaussian quantum states in quantum optics and beyond.
Non-Gaussian quantum states of light are essential resources for quantum information processing and precision metrology. Among them, generalized coherent states (GCS), which naturally arise from the evolution of a coherent state with a nonlinear medium, exhibit useful quantum features such as Wigner negativity and metrological advantages [Phys. Rev. Res. 5, 013165 (2023)]. Because these states remain coherent to all orders, their nonclassical character cannot be revealed through standard intensity-intensity correlation measurements. Here, we demonstrate that the intensity-field correlation function alone provides a simple and experimentally accessible witness of nonclassicality. For GCSs, any deviation of this normalized correlation from unity signals nonclassical behavior. We derive analytical results for Kerr-generated states and extend the analysis to statistical mixtures of GCSs. The proposed approach enables real-time, low-complexity detection of quantum signatures in non-Gaussian states, offering a practical tool for experiments across a broad range of nonlinear regimes.