Local deterministic model of singlet state correlations based on relaxing measurement independence

TL;DR

This paper presents a local deterministic model for singlet state correlations that relaxes measurement independence, showing that a small loss of free will in measurement choices can reproduce quantum correlations and violate Bell inequalities.

Contribution

It introduces a simple measure of measurement independence and demonstrates that singlet correlations can be modeled with minimal relaxation of this assumption, challenging traditional views.

Findings

Singlet correlations can be modeled with only 14% measurement independence loss.

A local deterministic model achieves maximal Bell-CHSH violation with 33% measurement independence.

The model is deterministic, no-signalling, and requires less relaxation of assumptions than previous models.

Abstract

The derivation of Bell inequalities requires an assumption of measurement independence, related to the amount of free will experimenters have in choosing measurement settings. Violation of these inequalities by singlet state correlations, as has been experimentally observed, brings this assumption into question. A simple measure of the degree of measurement independence is defined for correlation models, and it is shown that all spin correlations of a singlet state can be modeled via giving up a fraction of just 14% of measurement independence. The underlying model is deterministic and no-signalling. It may thus be favourably compared with other underlying models of the singlet state, which require maximum indeterminism or maximum signalling. A local deterministic model is also given that achieves the maximum possible violation of the well known Bell-CHSH inequality, at a cost of only 1/3 of measurement independence.