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This research presents an efficient method for visualizing quantum nonlocality across spatially multimode fields by combining metasurfaces with adaptive neural networks. The approach significantly reduces measurement costs, enabling large-scale Bell certification and advancing practical applications in quantum imaging and networking. By mapping the two-dimensional distribution of entanglement violations, this work offers a scalable pathway for exploiting complex photonic states without prohibitive resource overheads.
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Spatial nonlocality imaging via metasurface

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arXiv:2607.17618v1 Announce Type: new Abstract: Bell nonlocality is both a defining signature of entanglement and a key quantum information resource. However, visualizing and certifying nonlocal correlations across a spatially multimode photonic field remains challenging due to the rapidly growing measurement cost of spatially resolved projective tests. To address this issue, we build a spatial nonlocality imaging scheme that directly reveals the spatial distribution of quantum nonlocality by integrating a metasurface that performs parallel polarization projections with a quantum-adaptive neural network. Spatially resolved Clauser--Horne--Shimony--Holt (CHSH) tests are realized over a 400-pixel biphoton field using an average of only 1.7 detected coincidence pairs per pixel per basis. This approach yields a nonlocality image that maps the two-dimensional spatial distribution of Bell violations across the optical field and reveals the target-state-dependent spatial evolution of Bell violations. It provides a highly resource-efficient route to large-scale Bell certification and opens new possibilities for exploiting spatially multimode entanglement in quantum imaging, quantum networking, and scalable photonic quantum technologies.

Abstract:Bell nonlocality is both a defining signature of entanglement and a key quantum information resource. However, visualizing and certifying nonlocal correlations across a spatially multimode photonic field remains challenging due to the rapidly growing measurement cost of spatially resolved projective tests. To address this issue, we build a spatial nonlocality imaging scheme that directly reveals the spatial distribution of quantum nonlocality by integrating a metasurface that performs parallel polarization projections with a quantum-adaptive neural network. Spatially resolved Clauser--Horne--Shimony--Holt (CHSH) tests are realized over a 400-pixel biphoton field using an average of only 1.7 detected coincidence pairs per pixel per basis. This approach yields a nonlocality image that maps the two-dimensional spatial distribution of Bell violations across the optical field and reveals the target-state-dependent spatial evolution of Bell violations. It provides a highly resource-efficient route to large-scale Bell certification and opens new possibilities for exploiting spatially multimode entanglement in quantum imaging, quantum networking, and scalable photonic quantum technologies.

18 pages, 5 figures, with 21 pages of Supplementary Materials. Comments are welcome; please contact the corresponding authors for inquiries

Quantum Physics (quant-ph); Optics (physics.optics)

arXiv:2607.17618 [quant-ph]

(or arXiv:2607.17618v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.17618 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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