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

TL;DR

This paper establishes conditions under which post-selection in quantum networks preserves the integrity of Bell tests, ensuring loophole-free nonlocality demonstrations even with unreliable sources.

Contribution

It introduces a formal criterion for fair-sampling in quantum networks, linking it to the saturation of the Finner inequality for self-testing and improving device-independent randomness.

Findings

Post-selection can be loophole-free under fair-sampling conditions.

Saturation of the Finner inequality self-tests the quantum model.

Improved device-independent randomness in photonic Bell tests.

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.