Bulk-boundary correspondence, a central principle in topological matter relating bulk topological invariants to edge states, breaks down in a generic class of non-Hermitian systems that have so far eluded experimental effort. Here we theoretically predict and experimentally observe non-Hermitian bulk-boundary correspondence, a fundamental generalization of the conventional bulk-boundary correspondence, in discrete-time non-unitary quantum-walk dynamics of single photons. We experimentally demonstrate 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 match excellently with non-Bloch topological invariants calculated from localized bulk-state wave functions. 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.

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We experimentally realize a nonlinear quantum protocol on single-photon qubits with linear optical elements and appropriate measurements. The quantum nonlinearity is induced by post-selecting the polarization qubit based on a measurement result obtained on the spatial degree of freedom of the single photon which plays the role of a second qubit. Initially, both qubits are prepared in the same quantum state and an appropriate two-qubit unitary transformation entangles them before the measurement on the spatial part. We analyze the result by quantum state tomography on the polarization degree of freedom. We then demonstrate the usefulness of the protocol for quantum state discrimination by iteratively applying it on either one of two slightly different quantum states which rapidly converge to different orthogonal states by the iterative dynamics. Our work opens the door to employ effective quantum nonlinear evolution for quantum information processing.

The Clauser–Horne–Shimony–Holt (CHSH) inequality test is widely used as a mean of invalidating the local deterministic theories. Most attempts to experimentally test nonlocality have presumed unphysical idealizations that do not hold in real experiments, namely, noiseless measurements. We demonstrate an experimental violation of the CHSH inequality that is free of idealization and rules out local models with high confidence. We show that the CHSH inequality can always be violated for any nonzero noise parameter of the measurement. Intriguingly, less entanglement exhibits more nonlocality in the CHSH test with noisy measurements. Furthermore, we theoretically propose and experimentally demonstrate how the CHSH test with noisy measurements can be used to detect weak entanglement on two-qubit states. Our results offer a deeper insight into the relation between entanglement and nonlocality.