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Automated generation of photonic circuits for Bell tests with homodyne measurements

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Researchers developed an AI-driven framework combining deep reinforcement learning and quantum optics simulations to automatically design photonic circuits for Bell tests, achieving a CHSH violation of 2.068 with minimal hardware. The system uses homodyne detectors—practical, room-temperature devices operating at telecom wavelengths—unlike bulky setups in previous experiments, enabling real-world quantum communication applications. A key breakthrough is a four-mode circuit with just two squeezed light sources (3.9 dB and 0.008 dB) and two beam splitters, simplifying experimental requirements while maintaining robustness. The design sustains Bell violations over 8 km of optical fiber and tolerates heralding detector inefficiencies, making it viable for loophole-free tests and chip-integrated quantum technologies. This work advances device-independent protocols by demonstrating scalable, loss-resistant photonic architectures, bridging the gap between theory and practical quantum networks.

Automated generation of photonic circuits for Bell tests with homodyne measurements

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AbstractNonlocal quantum realizations, certified by the violation of a Bell inequality, are core resources for device-independent quantum information processing. Although proof-of-principle experiments demonstrating device-independent quantum information processing have already been reported, identifying physical platforms that are realistically closer to practical, viable devices remains a significant challenge. In this work, we present an automated framework for designing photonic implementations of nonlocal realizations using homodyne detections and quantum state heralding. Combining deep reinforcement learning and efficient simulations of quantum optical processes, our method generates photonic circuits that achieve significant violations of the Clauser-Horne-Shimony-Holt inequality. In particular, we find an experimental setup, robust to losses, that yields a CHSH violation of $2.068$ with $3.9$ dB and $0.008$ dB squeezed light sources and two beam splitters.Popular summaryQuantum mechanics predicts that two particles can be entangled, allowing them to exhibit correlations that no classical system can reproduce. The existence of such nonlocal correlations can be confirmed through violations of Bell inequalities. Harnessing this nonlocality is essential for secure quantum communication and other device-independent quantum technologies. However, many experimental realizations of Bell tests and device-independent protocols require complex and bulky machinery, making them poorly suited for practical or commercial applications. In this work, we present an automated method that combines search algorithms with efficient quantum optics simulations, to discover photonic circuits capable of violating the CHSH Bell inequality using homodyne detectors ; a particularly practical type of detector that operates at telecom wavelengths and at room temperature. By exploring a wide range of possible circuit configurations, our method identifies several promising designs. Most notably, we report a simple four-mode circuit using two squeezed light sources, two beam splitters, and a heralding mechanism, which yields a CHSH score of $2.068$. This circuit maintains a Bell violation over distances exceeding $8$ kilometers of optical fiber and remains robust to inefficiencies in the heralding detectors, making it a realistic candidate for a first loophole-free Bell test based on homodyne measurements and a promising step toward practical, chip-integrated implementations of device-independent protocols.► BibTeX data@article{Lanore2026automatedgeneration, doi = {10.22331/q-2026-03-10-2021}, url = {https://doi.org/10.22331/q-2026-03-10-2021}, title = {Automated generation of photonic circuits for {B}ell tests with homodyne measurements}, author = {Lanore, Corentin and Grasselli, Federico and Valcarce, Xavier and Bancal, Jean-Daniel and Sangouard, Nicolas}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2021}, month = mar, year = {2026} }► References [1] J. S. Bell. ``On the Einstein Podolsky Rosen paradox''.

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PRX Quantum 2, 030204 (2021). https://doi.org/10.1103/PRXQuantum.2.030204 [55] Corentin Lanore, Federico Grasselli, and Xavier Valcarce. code: JuliaReinforcementLearning/ReinforcementLearning.jl. https://github.com/JuliaReinforcementLearning/ReinforcementLearning.jl [56] Xavier Valcarce. code: xvalcarce/QuantumOpticalCircuits.jl. https://github.com/xvalcarce/QuantumOpticalCircuits.jl [57] Jun Tian and other contributors. code: JuliaReinforcementLearning/ReinforcementLearning.jl. https://github.com/JuliaReinforcementLearning/ReinforcementLearning.jl [58] Werner Vogel and Dirk‐Gunnar Welsch. ``Quantum optics''. Wiley. (2006). https://doi.org/10.1002/3527608524 [59] Stefano Pirandola, Alessio Serafini, and Seth Lloyd. ``Correlation matrices of two-mode bosonic systems''. Phys. Rev. A 79, 052327 (2009). https://doi.org/10.1103/PhysRevA.79.052327 [60] Jun Tian and other contributors (2020). code: JuliaReinforcementLearning/ReinforcementLearning.jl commit:b4c9f40. https://github.com/JuliaReinforcementLearning/ReinforcementLearning.jl/blob/b4c9f404be5b921178fbee34f93a00dd143a829a/src/ReinforcementLearningZoo/src/algorithms/policy_gradient/ppo.jl [61] Nicolas Brunner, Nicolas Gisin, Valerio Scarani, and Christoph Simon. ``Detection loophole in asymmetric bell experiments''. Phys. Rev. Lett. 98, 220403 (2007). https://doi.org/10.1103/PhysRevLett.98.220403 [62] Adán Cabello and Jan-Åke Larsson. ``Minimum detection efficiency for a loophole-free atom-photon bell experiment''. Phys. Rev. Lett. 98, 220402 (2007). https://doi.org/10.1103/PhysRevLett.98.220402Cited byCould not fetch Crossref cited-by data during last attempt 2026-03-10 14:52:47: Could not fetch cited-by data for 10.22331/q-2026-03-10-2021 from Crossref. This is normal if the DOI was registered recently. Could not fetch ADS cited-by data during last attempt 2026-03-10 14:52:47: No response from ADS or unable to decode the received json data when getting the list of citing works.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractNonlocal quantum realizations, certified by the violation of a Bell inequality, are core resources for device-independent quantum information processing. Although proof-of-principle experiments demonstrating device-independent quantum information processing have already been reported, identifying physical platforms that are realistically closer to practical, viable devices remains a significant challenge. In this work, we present an automated framework for designing photonic implementations of nonlocal realizations using homodyne detections and quantum state heralding. Combining deep reinforcement learning and efficient simulations of quantum optical processes, our method generates photonic circuits that achieve significant violations of the Clauser-Horne-Shimony-Holt inequality. In particular, we find an experimental setup, robust to losses, that yields a CHSH violation of $2.068$ with $3.9$ dB and $0.008$ dB squeezed light sources and two beam splitters.Popular summaryQuantum mechanics predicts that two particles can be entangled, allowing them to exhibit correlations that no classical system can reproduce. The existence of such nonlocal correlations can be confirmed through violations of Bell inequalities. Harnessing this nonlocality is essential for secure quantum communication and other device-independent quantum technologies. However, many experimental realizations of Bell tests and device-independent protocols require complex and bulky machinery, making them poorly suited for practical or commercial applications. In this work, we present an automated method that combines search algorithms with efficient quantum optics simulations, to discover photonic circuits capable of violating the CHSH Bell inequality using homodyne detectors ; a particularly practical type of detector that operates at telecom wavelengths and at room temperature. By exploring a wide range of possible circuit configurations, our method identifies several promising designs. Most notably, we report a simple four-mode circuit using two squeezed light sources, two beam splitters, and a heralding mechanism, which yields a CHSH score of $2.068$. This circuit maintains a Bell violation over distances exceeding $8$ kilometers of optical fiber and remains robust to inefficiencies in the heralding detectors, making it a realistic candidate for a first loophole-free Bell test based on homodyne measurements and a promising step toward practical, chip-integrated implementations of device-independent protocols.► BibTeX data@article{Lanore2026automatedgeneration, doi = {10.22331/q-2026-03-10-2021}, url = {https://doi.org/10.22331/q-2026-03-10-2021}, title = {Automated generation of photonic circuits for {B}ell tests with homodyne measurements}, author = {Lanore, Corentin and Grasselli, Federico and Valcarce, Xavier and Bancal, Jean-Daniel and Sangouard, Nicolas}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2021}, month = mar, year = {2026} }► References [1] J. S. Bell. ``On the Einstein Podolsky Rosen paradox''.

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Automated generation of photonic circuits for Bell tests with homodyne measurements

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