Investigation of nonlocal information as condition for violations of Bell inequality and information causality

TL;DR

This paper proves that mutual information about distant outcomes and measurement settings is essential for violating Bell's inequality and information causality, highlighting the role of nonlocal information under different measurement biases.

Contribution

It establishes the necessity of mutual information about outcomes and settings for violations of Bell's inequality and information causality, considering measurement biases and free measurement choices.

Findings

Mutual information about distant outcomes is necessary for Bell violation with unbiased marginals.

Mutual information about distant measurement settings remains necessary even with biased marginals.

Both types of mutual information are required for violating information causality.

Abstract

On the basis of local realism theory, nonlocal information is necessary for violation of Bell's inequality. From a theoretical point of view, nonlocal information is essentially the mutual information on distant outcome and measurement setting. In this work we prove that if the measurement is free and unbiased, the mutual information about the distant outcome and setting is both necessary for the violation of Bell's inequality in the case with unbiased marginal probabilities. In the case with biased marginal probabilities, we point out that the mutual information about distant outcome cease to be necessary for violation of Bell's inequality, while the mutual information about distant measurement settings is still required. We also prove that the mutual information about distant measurement settings must be contained in the transmitted messages due to the freedom of measurement choices. Finally we point out that the mutual information about both distant outcome and measurement settings are necessary for a violation of information causality.