Arbitrarily small amount of measurement independence is sufficient to manifest quantum nonlocality

TL;DR

This paper demonstrates that even minimal measurement independence is enough to reveal quantum nonlocality in Bell tests, challenging assumptions about free measurement choices in quantum experiments.

Contribution

It introduces the concept of measurement dependent locality and characterizes the resulting correlations with Bell-like inequalities, enabling analysis under limited measurement independence.

Findings

Arbitrarily small measurement independence suffices to manifest nonlocality.

Correlations form a convex polytope, allowing efficient characterization.

Systematic study of nonlocality with limited measurement independence is possible.

Abstract

The use of Bell's theorem in any application or experiment relies on the assumption of free choice or, more precisely, measurement independence, meaning that the measurements can be chosen freely. Here, we prove that even in the simplest Bell test - one involving 2 parties each performing 2 binary-outcome measurements - an arbitrarily small amount of measurement independence is sufficient to manifest quantum nonlocality. To this end, we introduce the notion of measurement dependent locality and show that the corresponding correlations form a convex polytope. These correlations can thus be characterized efficiently, e.g., using a finite set of Bell-like inequalities - an observation that enables the systematic study of quantum nonlocality and related applications under limited measurement independence.