Tractable protocol for detection-loophole-free Bell tests over long distances
Bibliographic record
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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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".