Quantum nonlocality in presence of strong measurement dependence

TL;DR

This paper investigates the minimal measurement independence required to observe quantum nonlocality, demonstrating that nonlocality persists even with nearly fully determined measurement choices, with implications for randomness amplification.

Contribution

It introduces models with strong measurement dependence where quantum nonlocality still appears, suggesting this is near the minimal measurement independence needed.

Findings

Quantum nonlocality persists with almost fully determined measurement choices.

Models with strong measurement dependence can still violate Bell inequalities.

Potential applications in randomness amplification are discussed.

Abstract

It is well known that the effect of quantum nonlocality, as witnessed by violation of a Bell inequality, can be observed even when relaxing the assumption of measurement independence, i.e. allowing for the source to be partially correlated with the choices of measurement settings. But what is the minimal amount of measurement independence needed for observing quantum nonlocality? Here we explore this question and consider models with strong measurement-dependent locality, where measurement choices can be perfectly determined in almost all rounds of the Bell test. Yet, we show that quantum nonlocality can still be observed in this scenario, which we conjecture is minimal within the framework we use. We also discuss potential applications in randomness amplification.