Measurement-dependent locality beyond i.i.d

TL;DR

This paper explores measurement-dependent locality in Bell tests beyond the i.i.d. assumption, demonstrating that non-i.i.d. models are more powerful and discussing implications for randomness amplification.

Contribution

It introduces a polytope for block-i.i.d. measurement-dependent local models and proves their greater power over i.i.d. models.

Findings

Non-i.i.d. models are strictly more powerful than i.i.d. models.

The work extends the understanding of measurement dependence in Bell tests.

Implications for randomness amplification in Bell scenarios.

Abstract

When conducting a Bell test, it is normal to assume that the preparation of the quantum state is independent of the measurements performed on it. Remarkably, the violation of local realism by entangled quantum systems can be certified even if this assumption is partially relaxed. Here, we allow such measurement dependence to correlate multiple runs of the experiment, going beyond previous studies that considered independent and identically distributed (i.i.d.) runs. To do so, we study the polytope that defines block-i.i.d. measurement-dependent local models. We prove that non-i.i.d. models are strictly more powerful than i.i.d. ones, and comment on the relevance of this work for the study of randomness amplification in simple Bell scenarios with suitably optimised inequalities.