Nonlocal setting and outcome information for violation of Bell's inequality

TL;DR

This paper analyzes the conditions necessary to violate Bell's inequality, emphasizing the role of nonlocal information about settings and outcomes, and quantifies the information transfer needed for maximal violation.

Contribution

It provides a novel analysis showing that violating Bell's inequality requires nonlocal transfer of both setting and outcome information, even under assumptions of realism and freedom of choice.

Findings

Maximum violation requires 0.736 bits of nonlocal setting information.

Both setting and outcome information must be nonlocally transferred to violate Bell's inequality.

Outcome information can be shared via hidden variables, but setting information must be nonlocal.

Abstract

Bell's theorem is a no-go theorem stating that quantum mechanics cannot be reproduced by a physical theory based on realism, freedom to choose experimental settings and two locality conditions: setting (SI) and outcome (OI) independence. We provide a novel analysis of what it takes to violate Bell's inequality within the framework in which both realism and freedom of choice are assumed, by showing that it is impossible to model a violation without having information in one laboratory about both the setting and the outcome at the distant one. While it is possible that outcome information can be revealed from shared hidden variables, the assumed experimenter's freedom to choose the settings forces that setting information must be non-locally transferred, even when the SI condition is obeyed. The sufficient amount of transmitted information about the setting to violate the CHSH inequality up to its quantum mechanical maximum is 0.736 bits.