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  • Open Access

Tractable protocol for detection-loophole-free Bell tests over long distances

Yazeed K. Alwehaibi*, Ewan Mer, Gerard J. Machado, Shang Yu, Ian A. Walmsley, and Raj B. Patel†

  • Blackett Laboratory, Department of Physics, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom and Centre for Quantum Engineering, Science and Technology (QuEST), Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom

  • *Contact author: y.alwehaibi23@imperial.ac.uk
  • †Contact author: raj.patel1@imperial.ac.uk
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Phys. Rev. Research 7, 043198 – Published 20 November, 2025

DOI: https://doi.org/10.1103/xw66-nqfs

Abstract

Certifying genuine nonclassical correlations over long distances is essential for device-independent quantum information. In photonic platforms, however, this remains challenging due to photon loss, which opens the detection loophole, rendering violations increasingly difficult for less-efficient detectors. Eberhard showed that using nonmaximally entangled states lowers the detection-efficiency threshold to 66.7%, but existing photonic approaches are restricted to short distances with linear transmittance scaling. Conversely, single-photon event-ready schemes extend the distance with favorable square-root scaling with channel transmittance, yet still demand detection efficiencies above 82.6%. Here, we propose the first all-photonic, heralded entanglement distribution protocol that unifies these two advances: It achieves a postselection-free violation at the Eberhard limit while preserving twin-field-like scaling. We identify the loss independent of the vacuum component amplitude of the prepared state as the source of this enhancement. Our approach addresses both resilience to loss and scalability, providing a practical route toward long-distance, loophole-free Bell tests and device-independent applications with current technology.

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Phys. Rev. Research 7, 043198– Published 20 November, 2025
  • Received 17 June 2025
  • Accepted 21 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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