How to reveal topological phases and their boundaries is an intriguing issue in various systems. Entanglement, which plays a fundamental role in quantum information, has been found profoundly related to topological phases. However, experimentally exploring this relation is precluded by the limited ability to obtain entanglement in many-body systems. In this work, we propose and experimentally demonstrate that the robustness of entanglement, quantified by the von Neumann entropy, can be used to reveal the topological phase with winding number $ {\cal W} = 1 $ and topological phase with $ {\cal W} = 0 $ in quantum walks. With the different robustness of entanglement against perturbations of a parameter, the phase boundaries between the distinct topological phases can be further determined. As a result, our work not only offers a new perspective for quantum walks but also exhibits the deep connection between entanglement and topological physics.

中文翻译：

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纠缠的稳健性是量子行走中拓扑相位的指标

在各种系统中，如何揭示拓扑阶段及其边界是一个有趣的问题。纠缠在量子信息中起着根本性的作用，已被发现与拓扑阶段密切相关。但是，在多体系统中获得纠缠的能力有限，因此无法通过实验探索这种关系。在这项工作中，我们提出并通过实验证明，由冯·诺伊曼熵量化的纠缠的鲁棒性可用于揭示绕组数为$ {\ cal W} = 1 $的拓扑相和$ {\ cal W} = 0 $在量子行走中。利用纠缠对参数扰动的不同鲁棒性，可以进一步确定不同拓扑相位之间的相位边界。结果，我们的工作不仅为量子行走提供了新的视角，而且展现了纠缠与拓扑物理学之间的深层联系。