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Certifying Non-Classicality and Non-Gaussianity Through Optical Parametric Amplification

Mahmoud Kalash, M. H. M. Passos, Éva Rácz, László Ruppert, Radim Filip, Maria V. Chekhova

Published Jun 3, 2026• 1 citation
Publisher

Abstract

Non-Gaussian states of light are essential for numerous quantum information protocols; thus, certifying non-Gaussianity (NG) is crucial. Full quantum state tomography, commonly used for this purpose, is complicated and yields inconclusive results for strongly mixed states. Certifying NG through directly measurable parameters is a simpler alternative, typically achieved by measuring photon-number probabilities—either directly, using photon-number resolving detectors, or through Hanbury Brown-Twiss type measurements with single-photon detectors. Here, we demonstrate, theoretically and experimentally, that phase-sensitive optical parametric amplification (OPA), followed by conventional intensity detection, can effectively replace this approach. Our proposed witness relies on the mean photon number (relative to that produced by the amplifier without any input) and the second-order correlation function after OPA. Both can be directly obtained from the measured amplified intensity and are invariant to detection losses. The method therefore requires neither photon-number resolution nor high detection efficiency. In a proof-of-principle experiment, we successfully certify the quantum NG of a heralded quasi-single-photon state. Since OPA is a broadband and multimode process, our method provides a foundation for developing high-dimensional quantum technologies utilizing broadband multimode non-Gaussian states.

DOI
10.1103/j68x-skmn

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Non-Gaussian states of light are essential for numerous quantum information protocols; thus, certifying non-Gaussianity (NG) is crucial. Full quantum state tomography, commonly used for this purpose, is complicated and yields inconclusive results for strongly mixed states. Certifying NG through directly measurable parameters is a simpler alternative, typically achieved by measuring photon-number probabilities—either directly, using photon-number resolving detectors, or through Hanbury Brown-Twiss type measurements with single-photon detectors. Here, we demonstrate, theoretically and experimentally, that phase-sensitive optical parametric amplification (OPA), followed by conventional intensity detection, can effectively replace this approach. Our proposed witness relies on the mean photon number (relative to that produced by the amplifier without any input) and the second-order correlation function after OPA. Both can be directly obtained from the measured amplified intensity and are invariant to detection losses. The method therefore requires neither photon-number resolution nor high detection efficiency. In a proof-of-principle experiment, we successfully certify the quantum NG of a heralded quasi-single-photon state. Since OPA is a broadband and multimode process, our method provides a foundation for developing high-dimensional quantum technologies utilizing broadband multimode non-Gaussian states.
Non-Gaussian states of light are essential for numerous quantum information protocols; thus, certifying non-Gaussianity is crucial. Full quantum state tomography, commonly used for this purpose, is a complicated procedure and yields inconclusive results for strongly mixed states. Certifying non-Gaussianity through directly measurable parameters is a simpler alternative, typically achieved by measuring photon-number probabilities - either directly, using photon-number resolving detectors, or through Hanbury Brown--Twiss type measurements with single-photon detectors. Here, we demonstrate theoretically and experimentally that optical parametric amplification combined with conventional intensity detectors can effectively replace this approach without the need for photon-number resolution. In our method, we measure the mean photon number and the second-order correlation function for the amplified state. Using it, we successfully certify the non-Gaussianity of a heralded quasi-single-photon state. Since optical parametric amplification is a broadband and multimode process, our method provides a foundation for developing high-dimensional quantum technologies utilizing broadband multimode non-Gaussian states.
Optical quantum information science plays a central role in the development of advanced photonic technologies, with applications ranging from quantum imaging and communication to continuous-variable (CV) quantum computing. The efficient realization of these technologies depends not only on the generation of nonclassical states of light but also on their proper detection. Optical parametric amplification (OPA) has long been known as both a fundamental nonlinear process for generating nonclassical light and as a method to boost detection efficiency through pre-amplification. Recently, OPA has been revisited as a tool for all-optical quadrature detection, offering a powerful alternative to conventional homodyne detection by enabling broadband, loss-tolerant squeezing measurements across various optical platforms. In this thesis, I establish optical parametric amplification as a versatile tool for the detection of CV quantum states through all-optical quadrature detection. I extend squeezing detection to high-dimensional scenarios by exploiting the intrinsic multimode nature of OPA, thereby enabling, for the first time to the best of my knowledge, the real-time monitoring of multimode squeezed light, a long-standing challenge in quantum optics. This approach further permits the simultaneous monitoring of multiple CV Einstein–Podolsky–Rosen (EPR) mode pairs, providing a framework for scalable detection of multimode entanglement, namely optical cluster states, which constitute essential resources for CV quantum computing. Furthermore, I demonstrate OPA as a platform for loss-tolerant and broadband quantum state tomography, applying it to both Gaussian and non-Gaussian states. This paves the way for the scalable tomography of multimode quantum states. Finally, I show that OPA enables the certification of the non-Gaussian and nonclassical character of quantum states without the need for photon-number-resolving detectors, relying instead on post-amplification intensity statistics. In particular, I amplify a single photon sufficiently strongly that its non-Gaussian character becomes accessible through conventional intensity detectors. Altogether, this work establishes optical parametric amplification as a powerful and scalable platform for high-dimensional continuous-variable optical quantum technologies.
Characterizing non-Gaussian quantum states is of paramount importance for continuous-variable quantum information processing, yet conventional homodyne-measurement-based state tomography remains limited by optical loss, detector efficiency, and measurement bandwidth. Here, we introduce an integrated framework for loss-tolerant characterization and certification using high-gain phase-sensitive optical parametric amplification and power measurements. Our computationally efficient semidefinite programming approach enables faithful reconstruction of parity-symmetric quantum states from amplified quadrature measurements while substantially relaxing detector-efficiency requirements and increasing the measurement bandwidth. We further develop a certification framework that directly quantifies non-Gaussianity via stellar-rank witnesses and Wigner negativity, using the same quadrature-power measurements. We demonstrate the efficacy of the proposed framework through both simulated and experimental data for representative quantum states, including single-photon, Schrodinger cat, and Gottesman-Kitaev-Preskill (GKP) states. By unifying loss-tolerant measurements, state tomography, and nonclassical-state certification within a single experimentally accessible framework, our approach provides a practical pathway toward verifying increasingly complex states and can be readily implemented with current quantum photonic technologies.
Current advances in nonlinear optics have made it possible to perform a homodyne-like tomography of an unknown state without highly efficient detectors or a strong local oscillator. Thereby, a new experimental direction has been opened into multimode and large-bandwidth quantum optics. An optical parametric amplifier (OPA) allows us to reconstruct the quadrature distribution of an unknown state directly from the measured intensity distribution with high precision. We propose adding a controllable displacement to the standard scheme, obtaining an improved method applicable even to asymmetric and non-Gaussian states while significantly increasing estimation accuracy and lowering the OPA amplification requirement. To demonstrate the power of our method, we accurately detect the sub-Planck phase-space structure by a distillable squeezing from the OPA estimates of various non-Gaussian states. With the improvements, OPA tomography became a generally applicable loss-tolerant and efficient alternative to OPA-assisted homodyne detection.
Abstract Current advances in nonlinear optics have made it possible to perform a homodyne-like tomography of an unknown state without highly efficient detectors or a strong local oscillator. Thereby, a new experimental direction has been opened into multimode and large-bandwidth quantum optics. An optical parametric amplifier (OPA) allows us to reconstruct the quadrature distribution of an unknown state directly from the measured intensity distribution with high precision. We propose adding a controllable displacement to the standard scheme, thus, obtaining a method applicable even to asymmetric and non-Gaussian states while significantly increasing estimation accuracy and lowering the OPA amplification requirement. To demonstrate the power of our method, we accurately detect the sub-Planck phase-space structure by obtaining distillable squeezing from the OPA estimates of various non-Gaussian states. With the improvements, OPA tomography became a generally applicable loss-tolerant and efficient alternative to homodyne detection.
Direct measurement of quantum non-Gaussianity requires some variant of a discrete photon-resolving detection, which is feasible only for low mean photon numbers. For a large mean photon number, intensity detection by linear photodiodes provides a continuous signal; therefore, the Fock probabilities of the unknown input state are not directly available. On the other hand, intensity moments can be measured directly, and photon-number moments can be estimated. Therefore, we derive and analyze a quantum non-Gaussianity witness based solely on the photon-number mean and variance (or alternatively, the second-order correlation g ( 2 ) ) of an unknown state. Due to the simplicity of the used photon-number moments, the measurement results are easy to correct for losses and additive noise. We provide examples of simple amplification-based measurement schemes where our witness can be applied directly, thereby opening pathways to proof-of-principle tests and applications.