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Chinese Physics B

Non-Gaussianity detection of single-mode rotationally symmetric quantum states via cumulant method

Shao-Hua Xiang, Li-Jun 利军 Huang 黄, Xian Wu Mi

Published Feb 2, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/ad2506

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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.
Covariance matrices lie at the heart of the powerful and well-established symplectic framework for describing continuous-variable Gaussian quantum states. However, since this framework only relies on first- and second-order moments, it is not sufficient for the analysis of non-Gaussian states because their higher-order moments are essential to capture some of their key properties. Here, we define higher-order covariance matrices -- more precisely, covariance matrices built from higher-order quadrature monomials -- which provide a simple way to evaluate the effect of Gaussian transformations on non-Gaussian states and can be used, for example, to address nonlinear squeezing or non-Gaussian nullifiers. Higher-order covariance matrices can be estimated from homodyne measurement data using only a limited number of quadrature angles, which involves matrices of moderate dimension compared with a full simulation in the Fock basis. The dimension of a higher-order covariance matrix does not depend on the span of the quantum states in Fock basis and, furthermore, scales only polynomially with the number of modes.
Abstract Non-Gaussian quantum states are a known necessary resource for reaching a quantum advantage and for violating Bell inequalities in continuous variable systems. As one kind of manifestation of quantum correlations, Einstein–Podolsky–Rosen steering enables verification of shared entanglement even when one of the subsystems is not characterized. However, how to detect and classify such an effect for non-Gaussian states is far from being well understood. Here, we present an efficient non-Gaussian steering criterion based on the high-order observables and conduct a systematic investigation into the hierarchy of non-Gaussian steering criteria. Moreover, we apply our criterion to three experimentally-relevant non-Gaussian states under realistic conditions and, in particular, propose a feasible scheme to create multi-component cat states with tunable size by performing a suitable high-order quadrature measurement on the steering party. Our work reveals the fundamental characteristics of non-Gaussianity and quantum correlations, and offers new insights to explore their applications in quantum information processing.