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

Abstract

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 work, 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 optimal encoding operator that can 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 work provides a general framework for characterizing entanglement structures in diverse continuous variable systems, enabling a number of experimentally relevant applications.

Figures (3)

• Figure 1: Graph representation of different multipartite entanglement structures. As illustrated, a system with $N=4$ modes can be characterized by 15 different partitions, associated to different distributions of correlations as indicated by the solid circles. Each partition can be graphically represented by a Young tableau, where boxes in each row indicate correlated modes, while vertically stacked boxes indicate separable subsets.
• Figure 2: Multipartite entanglement structure detection. Without loss of generality, we randomly generated $10^4$ four-mode entangled states for each entanglement structure, classified according to Young diagram. The vertical axis shows the success rate of detecting this type of entanglement. The color denotes the order of the encoding operators $\mathbf{S}_j$ in QFI. The error bars represent the standard deviation of the detection rate, calculated by dividing these $10^4$ states into 10 sets.
• Figure 3: Witnessing fully inseparable entanglement for different non-Gaussian states. (a) The success rate of detecting entanglement for different multimode cases, where we randomly generated $10^4$ fully inseparable states of 3, 4, and 5 modes. The color denotes the order of the encoding operators in QFI. The error bars represent the standard deviation of the percentage of detecting fully inseparable states, calculated by dividing these $10^4$ states into 10 sets. (b) The percentage of detectable fully inseparable states in the presence of channel loss, where the dashed blue and solid green denote the QFI criterion based on first-order and second-order operators, respectively. (c) The witness of full inseparability using QFI based on the three-photon SPDC process, where we generated $10^4$ states with random nonlinear strengths and plotted the percentage of detectable full inseparable states using operators of different orders.