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.
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.
We report on direct experimental certification of the quantum non-Gaussian character of a photon number-resolving detector. The certification protocol is based on an adaptation of the existing quantum non-Gaussianity criteria for quantum states to quantum measurements. In our approach, it suffices to probe the detector with a vacuum state and two different thermal states to test its quantum non-Gaussianity. The certification is experimentally demonstrated for the detector formed by a spatially multiplexed array of ten single-photon avalanche photodiodes. We confirm the quantum non-Gaussianity of POVM elements Π ^ m associated with the m-fold coincidence counts, up to m = 7. The experimental ability to certify from the first principles the quantum non-Gaussian character of Π ^ m is for large m limited by low probability of the measurement outcomes, especially for vacuum input state. We find that the injection of independent Gaussian background noise into the detector can be helpful and may reduce the measurement time required for reliable confirmation of quantum non-Gaussianity. In addition, we modified and experimentally verified the quantum non-Gaussianity certification protocol employing a third thermal state instead of a vacuum to speed up the whole measurement. Our findings demonstrate the existence of efficient tools for the practical characterization of fundamental non-classical properties and benchmarking of complex optical quantum detectors.
A Quantum Non-Gaussianity Criterion Based on Photon Correlations g(2) and g(3)
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 g(3)+3g(2)≥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 g(3)+3g(2)=0.174(13), which represents a statistical significance of more than 100 standard deviations.
Highly nonclassical character of optical quantum detectors, such as single-photon detectors, is essential for preparation of quantum states of light and a vast majority of applications in quantum metrology and quantum information processing. Therefore, it is both fundamentally interesting and practically relevant to investigate the nonclassical features of optical quantum measurements. Here we propose and experimentally demonstrate a procedure for direct certification of quantum non-Gaussianity and Wigner function negativity, two crucial nonclassicality levels, of photonic quantum detectors. Remarkably, we characterize the highly nonclassical properties of the detector by probing it with only two classical thermal states and a vacuum state. We experimentally demonstrate the quantum non-Gaussianity of a single-photon avalanche diode even under the presence of background noise, and we also certify the negativity of the Wigner function of this detector. Our results open the way for direct benchmarking of photonic quantum detectors with a few measurements on classical 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.
We theoretically analyse the relation between non-Gaussianity and security of entanglement-based quantum key distribution (QKD) protocols, namely device-independent (DI) and entanglement-based BB84. A similar analysis has already been made for prepare-and-measure (P\&M) protocols \cite{Lasota2017}. In addition, we consider imperfect detection with dark counts and limited efficiency. We assume a perfect source of entangled Bell states as produced by quantum-dot type sources, depolarisation in the channel and different noise statistics, namely thermal and Poissonian. We consider single-photon avalanche photodiodes (SPAD) and photon number resolving detectors (PNRD) and use their respective criteria for non-Gaussianity. The results show cross-regions for both security and non-Gaussianity, hence, the possibility to conclude about the suitability of a given channel for secret key distribution. Our results can be useful as a pre-check for the implementation of QKD protocols.
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.