Correlations, Bell Inequality Violation & Quantum Entanglement

TL;DR

This paper reviews the relationship between quantum entanglement and Bell inequality violations, clarifying their connection and presenting new insights into how entanglement relates to nonclassical correlations in quantum physics.

Contribution

It offers a comprehensive review and new findings that clarify the role of entanglement in Bell inequality violations, addressing longstanding ambiguities.

Findings

Entanglement is necessary but not sufficient for Bell violation.

Some entangled states admit local hidden variable models.

New insights clarify the entanglement-Bell violation relationship.

Abstract

It is one of the most remarkable features of quantum physics that measurements on spatially separated systems cannot always be described by a locally causal theory. In such a theory, the outcomes of local measurements are determined in advance solely by some unknown (or hidden) variables and the choice of local measurements. Correlations that are allowed within the framework of a locally causal theory are termed classical. Typically, the fact that quantum mechanics does not always result in classical correlations is revealed by the violation of Bell inequalities, which are constraints that have to be satisfied by any classical correlations. It has been known for a long time that entanglement is necessary to demonstrate nonclassical correlations, and hence a Bell inequality violation. However, since some entangled quantum states are known to admit explicit locally causal models, the exact role of entanglement in Bell inequality violation has remained obscure. This thesis provides both a comprehensive review on these issues as well as a report on new discoveries made to clarify the relationship between entanglement and Bell inequality violation.