Characterizing Multipartite Non-Gaussian Entanglement for Three-Mode Spontaneous Parametric Down-Conversion Process

TL;DR

This paper introduces a practical method using nonlinear squeezing parameters to detect and classify multipartite non-Gaussian entanglement in continuous-variable quantum states, demonstrated through analysis of recent experimental data.

Contribution

It proposes an accessible approach to characterize multipartite non-Gaussian entanglement using optimized nonlinear squeezing parameters based on higher-order moments.

Findings

Nonlinear squeezing parameters effectively detect multipartite non-Gaussian entanglement.

The method approximates quantum Fisher information using third-order moments.

Application to experimental data confirms the method's practicality for state verification.

Abstract

Very recently, strongly non-Gaussian states have been observed via a direct three-mode spontaneous parametric down-conversion in a superconducting cavity [Phys. Rev. X 10, 011011 (2020)]. The created multi-photon non-Gaussian correlations are attractive and useful for various quantum information tasks. However, how to detect and classify multipartite non-Gaussian entanglement has not yet been completely understood. Here, we present an experimentally practical method to characterize continuous-variable multipartite non-Gaussian entanglement, by introducing a class of nonlinear squeezing parameters involving accessible higher-order moments of phase-space quadratures. As these parameters can depend on arbitrary operators, we consider their analytical optimization over a set of practical measurements, in order to detect different classes of multipartite non-Gaussian entanglement ranging from fully separable to fully inseparable. We demonstrate that the nonlinear squeezing parameters act as an excellent approximation to the quantum Fisher information within accessible third-order moments. The level of the nonlinear squeezing quantifies the metrological advantage provided by those entangled states. Moreover, by analyzing the above mentioned experiment, we show that our method can be readily used to confirm fully inseparable tripartite non-Gaussian entangled states by performing a limited number of measurements without requiring full knowledge of the quantum state.