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.
Highlights
Characterization and classification of quantum states of light represents one of the main topics in quantum optics since its early days and has remained an important subject of research today
We derive a quantum non-Gaussianity criterion based on the knowledge of vacuum probability and mean photon number of the state and we show that this latter criterion can be interpreted as a specific case of the above class of criteria considered in the limit T → 0
We have derived analytical criteria for quantum non-Gaussianity of optical quantum states based on measurements of vacuum probabilities of the input state and state attenuated with arbitrary transmittance T
Summary
Characterization and classification of quantum states of light represents one of the main topics in quantum optics since its early days and has remained an important subject of research today. We extend this approach to certification of quantum nonGaussianity and we derive a class of quantum non-Gaussianity criteria based on knowledge of probability of vacuum in the original state and in a state transmitted through a lossy channel with an arbitrary transmittance T. We provide a detailed mathematical proof that the resulting criteria are fully applicable to general multimode states with arbitrary number of modes This is crucial for their practical utilization, because in most photon counting experiments it is impossible to ensure that only a single mode is detected unless one employes a sophisticated and technically demanding temporal filtering via quantum pulse gating [43, 44]. We derive a quantum non-Gaussianity criterion based on the knowledge of vacuum probability and mean photon number of the state and we show that this latter criterion can be interpreted as a specific case of the above class of criteria considered in the limit T → 0. In the concluding part of the paper we discuss the scaling of the number of measurement events required for reliable confirmation of quantum nonGaussianity and compare performance of two setups that involve either one or two single-photon detectors
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