How much measurement independence is needed in order to demonstrate nonlocality?

TL;DR

This paper investigates how much measurement independence is necessary to demonstrate quantum nonlocality, showing that even minimal independence can reproduce quantum correlations, linking it to classical communication and detection loopholes.

Contribution

It establishes the minimal measurement independence required to reproduce singlet correlations, connecting it to classical communication and detection loopholes.

Findings

Reproduces singlet correlations with less than one bit of mutual information.

Links measurement dependence to classical communication models.

Shows even fully independent choices can reproduce quantum correlations.

Abstract

If nonlocality is to be inferred from a violation of Bell's inequality, an important assumption is that the measurement settings are freely chosen by the observers, or alternatively, that they are random and uncorrelated with the hypothetical local variables. We study the case where this assumption is weakened, so that measurement settings and local variables are at least partially correlated. As we show, there is a connection between this type of model and models which reproduce nonlocal correlations by allowing classical communication between the distant parties, and a connection with models that exploit the detection loophole. We show that even if Bob's choices are completely independent, all correlations obtained from projective measurements on a singlet can be reproduced, with the correlation (measured by mutual information) between Alice's choice and local variables less than or equal to a single bit.