Extending Bell's Theorem: Nonlocality via Measurement Dependence

TL;DR

This paper explores how relaxing measurement independence in Bell's theorem introduces potential signaling, and demonstrates that no-signaling constraints can lead to Bell inequalities without assuming measurement independence, impacting interpretations of quantum nonlocality.

Contribution

It extends Bell's theorem by showing measurement dependence violations relate to signaling and can be tested, providing a new perspective on quantum nonlocality without assuming measurement independence.

Findings

Violations of measurement independence can imply signaling.

No-signaling conditions allow Bell inequalities without measurement independence.

The Schulman model illustrates these concepts.

Abstract

Besides well-known conditions of locality or factorisability, deriving the Bell inequalities requires assuming that the distribution of hidden variables and Alice's and Bob's measurement settings be independent of each other. We show that (analogously to violations of locality due to action at a distance) certain violations of this Measurement Independence assumption can be associated with a notion of signalling in principle, thus making them also testable in principle, and spell out the appropriate conditions. Accordingly, we show that by imposing no-signalling one can prove a version of Bell's theorem that does not require the assumption of Measurement Independence. We discuss the "Schulman model" as an example, as well as lessons for "experimental metaphysics".