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arXiv · 2501.14027

Bell nonlocality in quantum networks with unreliable sources: Loophole-free postelection via self-testing

Sadra Boreiri·Nicolas Brunner·Pavel Sekatski
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Abstract

We discuss Bell nonlocality in quantum networks with unreliable sources. Our main result is a condition on the observed data which ensures that inconclusive events can be safely discarded, without introducing any loophole. More formally, we characterize the fair-sampling property for measurements in a network. When all measurements are fair-sampling, we show that the post-selection of conclusive outcomes does not compromise the assumption of source independence, hence avoiding the detection loophole. Furthermore, we show that in some cases, the fair-sampling property can in fact be guaranteed based only on observed data. To show this, we prove that saturation of the Finner inequality provides a self-test of the underlying quantum model. We illustrate the relevance of our results by demonstrating an improvement in device-independent randomness generation for a photonic Bell test with a probabilistic source and for the triangle network.

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Sadra Boreiri, Nicolas Brunner, Pavel Sekatski. 2025-01-23. Bell nonlocality in quantum networks with unreliable sources: Loophole-free postelection via self-testing. https://doi.org/10.1103/bqwm-ll5y

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