Robustness of entanglement as an indicator of topological phases in quantum walks

How to reveal topological phases and their boundaries is an intriguing issue in various systems. Entanglement, which plays fundamental role in quantum information, has been found profoundly related to the topological phases. However, experimentally exploring this relation is precluded by the limited ability to obtain the 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 $\mathcal{W}=1$ and topological phase with $\mathcal{W}=0$ 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 the entanglement and topological physics.