Extending the fair sampling assumption using causal diagrams

TL;DR

This paper analyzes the fair sampling assumption in Bell experiments using causal diagrams, providing a unified framework that clarifies its assumptions and extends its applicability to various experimental scenarios.

Contribution

It introduces a causal inference perspective on the fair sampling assumption, unifying different forms and extending its use to ideal and multipartite experiments.

Findings

The FSA can be interpreted through causal structures.

The FSA applies to ideal experiments with partial postselection.

The FSA is valid in multipartite nonlocality tests.

Abstract

Discarding undesirable measurement results in Bell experiments opens the detection loophole that prevents a conclusive demonstration of nonlocality. As closing the detection loophole represents a major technical challenge for many practical Bell experiments, it is customary to assume the so-called fair sampling assumption (FSA) that, in its original form, states that the collectively postselected statistics are a fair sample of the ideal statistics. Here, we analyze the FSA from the viewpoint of causal inference: We derive a causal structure that must be present in any causal model that faithfully encapsulates the FSA. This provides an easy, intuitive, and unifying approach that includes different accepted forms of the FSA and underlines what is really assumed when using the FSA. We then show that the FSA can not only be applied in scenarios with non-ideal detectors or transmission losses, but also in ideal experiments where only parts of the correlations are postselected, e.g., when the particles' destinations are in a superposition state. Finally, we demonstrate that the FSA is also applicable in multipartite scenarios that test for (genuine) multipartite nonlocality.