Characterizing the Multipartite Entanglement Structure of Non-Gaussian Continuous-Variable States with a Single Evolution Operator

Multipartite entanglement is an essential resource for quantum information tasks, but characterizing entanglement structures in continuous-variable systems remains challenging, especially in multimode non-Gaussian scenarios. In this Letter, we introduce an efficient method for detecting multipartite entanglement structures in continuous-variable states. Based on the quantum Fisher information, we propose a systematic approach to identify an encoding operator that can efficiently capture the quantum correlations in multimode non-Gaussian states. We demonstrate the effectiveness of our method on over 10^{5} randomly generated multimode-entangled quantum states, achieving a very high success rate in entanglement detection. Additionally, the robustness of our method can be considerably enhanced against losses by expanding the set of accessible operators. This Letter provides a general framework for characterizing entanglement structures in diverse continuous-variable systems, enabling a number of experimentally relevant applications.