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.
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18 pages, 5 figures, with 21 pages of Supplementary Materials. Comments are welcome; please contact the corresponding authors for inquiries
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.
Entangled photon pairs produced by spontaneous parametric down-conversion exhibit rich spatial entanglement structure that is often difficult to probe with conventional measurements. Here, we show that spin-orbit optical elements can convert this spatial structure into directly observable quantum interference patterns. Using a q-plate, we demonstrate that the relative wavefront curvature of biphoton states generated by a pair of nonlinear crystals can be retrieved from the spatial modulation of coincidence images. Building on this principle, we introduce a liquid-crystal metasurface that performs spatially multiplexed Bell measurements across the transverse profile of the photon field. The device, which we call a Clauser-Horne-Shimony-Holt (CHSH) plate, assigns different polarization projections to different azimuthal sectors of the beam, allowing the sixteen joint measurements required for a CHSH test to be realized simultaneously in a single acquisition. In this architecture, the spatial coordinate acts as a classical register selecting the measurement context, while photon pairs sample these contexts according to their emission directions. We further demonstrate that the same measurement concept can be implemented using a programmable spatial light modulator, providing a dynamically reconfigurable realization of the scheme. Our results show that spatially structured optical elements can transform Bell tests into parallel measurements distributed across the transverse plane, enabling rapid characterization of spatially varying entanglement. This approach opens new possibilities for structured-light quantum measurements, Bell-inequality-based imaging, and the study of spatially engineered entangled photon sources.
Quantum correlation between two parties serves as an important resource in the surging applications of quantum information. The Bell nonlocality and quantum steering have been proposed to describe non-classical correlations against local-hidden-variable and local-hidden-state theories, respectively. To characterize the two types of non-classical correlations, various nonlocality and steering inequalities have been established, and the amount of inequality violation serves as an important indicator for many entanglement-based tasks. Quantum state tomography has been employed for measuring quantum states, while the method requires intensive computation and does not directly verify either nonlocality or steering over the full domain independent of established theories. Here, we experimentally map the full-domain correlation with bipartite states for nonlocality and quantum steering in CHSH scenarios. The measurement of the maps automatically accounts for detection imperfections. Furthermore, we demonstrate the application of the correlation maps in the entanglement-based quantum key distribution protocol with arbitrary bipartite states. The correlation maps show direct measurements and simple interpretations that can answer fundamental questions about nonlocality and quantum steering as well as contribute to quantum information applications in a straightforward manner.
The concept of quantum entanglement and hyper-entanglement, lying at the heart of quantum information science and technologies, is physically counter-intuitive and mathematically elusive. We design a polarization-encoded ghost imaging system based on the frame of Hardy nonlocality paradox to visualize the evidence of quantum hyper-entanglement by capturing purely nonlocal photonic events. In two-photon polarization-spatial-mode hyper-entangled state, spatial entanglement con-veys the ghost images while polarization entanglement encodes the imaging channels. Then whether imaging the single ghost image of a skull-shape object or not can be a direct yet intuitive signature to support or defy quantum mechanics. We use the contrast-to-noise ratio of ghost images to macroscopically characterize the degree of the violation of locality. We also showcase the nonlocal behavior of violating the locality with a reasonable confidence level of 75%, microscopically at the single-pixel level. Our strategy not only sheds new light on the fundamental issue of quantum mechanics, but also holds promise for developing hyper-entanglement-based quantum imaging technology.
Abstract Optical hybrid entanglement can be created between two qubits, one encoded in a single photon and another one in coherent states with opposite phases. It opens the path to a variety of quantum technologies, such as heterogeneous quantum networks, merging continuous- and discrete-variable encoding, and enabling the transport and interconversion of information. However, reliable characterization of the non-local nature of this quantum state is limited so far to full quantum state tomography. Here, we perform a thorough study of Clauser–Horne–Shimony–Holt Bell inequality tests, enabling practical verification of quantum nonlocality for optical hybrid entanglement. We show that a practical violation of this inequality is possible with simple photon number on/off measurements if detection efficiencies stay above 82%. Another approach, based on photon-number parity measurements, requires 94% efficiency but works well in the limit of higher photon populations. Both tests use no postselection of the measurement outcomes and they are free of the fair-sampling hypothesis. Our proposal paves the way to performing loophole-free tests using feasible experimental tasks such as coherent state interference and photon counting.
Quantum-enhanced optical sensing leverages correlations and entanglement in multiphoton states to surpass the limitations of classical measurement. However, the widespread deployment of quantum imaging and polarimetry has been hindered by bulky nonlinear crystals, alignment-sensitive free-space optics, and limited control over the spatial and polarization structure of quantum light. This thesis investigates how engineered nanophotonic metasurfaces, together with two-photon probing schemes, can overcome these constraints and enable compact, versatile, and high-performance quantum sensing platforms. The first component of the thesis introduces a metasurface-enabled quantum imaging system based on spatially entangled photon pairs generated from a subwavelength-thick lithium niobate (LiNbO3) nonlinear metasurface. Exploiting nonlocal guided-mode resonances with strong angular dispersion, the system realizes a hybrid imaging protocol that combines quantum ghost imaging with all-optical wavelength-controlled scanning. A theoretical framework linking momentum-space biphoton correlations to image formation is developed, including the effects of pump-beam waist and metasurface quality factor. Numerical simulations and proof-of-principle experiments demonstrate 2D imaging with strong contrast and establish that metasurface-based photon-pair sources can achieve fields of view and resolution-cell counts far beyond what is possible with bulk-crystal SPDC. Building on this platform, the thesis presents the first quantum phase imaging system that integrates metasurfaces for both photon-pair generation and phase-gradient detection. A silicon (Si) metasurface with a near-linear optical transfer function directly maps phase gradients of transparent samples into spatial quantum correlations, eliminating the need for interferometers or long propagation paths. Experiments show that phase gradients up to 25rad/mm can be retrieved with high fidelity, and the system supports switchable operation between amplitude and phase imaging within a significantly more compact scale. The final component of the thesis develops a two-photon probing quantum polarimetry (TPQP) protocol for characterizing scattering media. By combining Monte Carlo modeling of microscopic photon trajectories with Mueller-matrix decomposition and quantum state tomography, the framework links entanglement degradation to macroscopic polarization observables and resolves ambiguities in Mueller-matrix extraction through tailored probe states. Experiments using tissue-mimicking phantoms confirm that TPQP exhibits significantly higher sensitivity to depolarization than one-photon probing, validating its potential for quantum-enhanced polarimetric sensing and imaging. Overall, this thesis advances quantum optical sensing through two distinct but complementary directions. The first two parts demonstrate how engineered metasurfaces enable compact quantum imaging and phase-gradient detection by integrating photon-pair generation and spatial processing within ultrathin nanophotonic structures. Independently, the two-photon probing quantum polarimetry framework, implemented using a conventional BBO-based entangled source, shows how nonlinear two-photon correlations can enhance sensitivity to depolarization and improve Mueller-matrix reconstruction in scattering media. Although realized on different physical platforms, all components of this work exploit quantum correlations to extract amplitude, phase, and polarization information beyond classical approaches, contributing to the development of practical quantum sensing methodologies.
Certification of nonlocality of quantum mechanics is an important fundamental test that typically requires prolonged data collection and is only revealed in an in-depth analysis. These features are often particularly exposed in hybrid systems, such as interfaces between light and atomic ensembles. Certification of entanglement from images acquired with single-photon camera can mitigate this issue by exploiting multiplexed photon generation. Here we demonstrate this feature in a quantum memory (QM) operating in a real-time feedback mode. Through spatially-multimode spin-wave storage the QM enables operation of the real-time ghost imaging (GI) protocol. By properly preparing the spatial phase of light emitted by the atoms we enable observation of Bell-type nonlocality from a single image acquired in the far field as witnessed by the Bell parameter of S=2.227±0.007>2 . Our results are an important step towards fast and efficient utilization of multimode quantum memories both in protocols and in fundamental tests.