A Tractable Protocol for Detection-Loophole-Free Bell Tests over Long Distances

TL;DR

This paper introduces a new protocol for long-distance Bell tests that overcomes detection loopholes by heralding entangled states with loss-independent vacuum components, enabling more practical device-independent quantum communication.

Contribution

The authors propose a heralded entanglement protocol that achieves loss-tolerant Bell violations without post-selection, using only quantum interference and single-photon detection.

Findings

Achieves Bell violation at the Eberhard limit with loss independence.

Requires only quantum interference at a central station.

Maintains square-root scaling with channel transmittance.

Abstract

Certifying genuine nonclassical correlations over long distances is crucial for device-independent (DI) quantum information protocols. However, in photonic platforms this remains technologically challenging due to photon loss, which opens the detection-loophole, rendering violations increasingly difficult for less efficient detectors. A well-known strategy to mitigate this involves using non-maximally entangled states, which Eberhard showed can tolerate lower detection efficiencies. However, existing proposals and demonstrations have been limited to short distances, as their success rates scale linearly with channel transmittance. Here, we propose a protocol to herald a tunable entangled state between distant users that achieves a post-selection-free Bell inequality violation at the Eberhard limit. We identify the loss independence of the vacuum component amplitude of the prepared state as the source of this enhancement. Notably, our scheme requires only quantum interference at a central station, followed by the detection of a single photon, preserving the optimal square-root scaling with channel transmittance. Our approach provides greater loss-tolerance in entanglement distribution, bringing long-distance DI applications closer to practical implementation.