Bulk–boundary correspondence, a guiding principle in topological matter, relates robust edge states to bulk topological invariants. Its validity, however, has so far been established only in closed systems. Recent theoretical studies indicate that this principle requires fundamental revisions for a wide range of open systems with effective non-Hermitian Hamiltonians. Therein, the intriguing localization of nominal bulk states at boundaries, known as the non-Hermitian skin effect, suggests a non-Bloch band theory in which non-Bloch topological invariants are defined in generalized Brillouin zones, leading to a general bulk–boundary correspondence beyond the conventional framework. Here, we experimentally observe this fundamental non-Hermitian bulk–boundary correspondence in discrete-time non-unitary quantum-walk dynamics of single photons. We demonstrate pronounced photon localizations near boundaries even in the absence of topological edge states, thus confirming the non-Hermitian skin effect. Facilitated by our experimental scheme of edge-state reconstruction, we directly measure topological edge states, which are in excellent agreement with the non-Bloch topological invariants. Our work unequivocally establishes the non-Hermitian bulk–boundary correspondence as a general principle underlying non-Hermitian topological systems and paves the way for a complete understanding of topological matter in open systems.

体边界对应是拓扑物质的指导原则，将鲁棒边缘状态与体拓扑不变量联系起来。然而，迄今为止，它的有效性仅在封闭系统中得到证实。最近的理论研究表明，该原理需要对具有有效非厄米哈密顿量的广泛开放系统进行根本性修改。其中，标称体态在边界处的有趣定位（称为非厄米集肤效应）提出了一种非布洛赫带理论，其中在广义布里渊区中定义了非布洛赫拓扑不变量，从而导致了一般体-边界对应超越常规框架。在这里，我们在单光子的离散时间非酉量子行走动力学中通过实验观察到这种基本的非厄米体边界对应。即使在没有拓扑边缘状态的情况下，我们也证明了边界附近明显的光子定位，从而证实了非厄米集肤效应。通过我们的边缘状态重建实验方案，我们直接测量拓扑边缘状态，这与非布洛赫拓扑不变量非常一致。我们的工作明确地将非厄米特体边界对应建立为非厄米特拓扑系统的一般原则，并为全面理解开放系统中的拓扑物质铺平了道路。这与非布洛赫拓扑不变量非常一致。我们的工作明确地将非厄米特体边界对应建立为非厄米特拓扑系统的一般原则，并为全面理解开放系统中的拓扑物质铺平了道路。这与非布洛赫拓扑不变量非常一致。我们的工作明确地将非厄米特体边界对应建立为非厄米特拓扑系统的一般原则，并为全面理解开放系统中的拓扑物质铺平了道路。