A unified view on Hardy's paradox and the CHSH inequality

TL;DR

This paper unifies Hardy's paradox and the CHSH inequality into a single framework of non-local games, enhancing understanding of quantum non-locality and its distinctions from classical correlations.

Contribution

It introduces a unified perspective that encompasses both Hardy's paradox and the CHSH inequality as special cases within a broader family of non-local games.

Findings

Unified framework for Hardy's paradox and CHSH inequality

Provides new insights into quantum non-locality

Bridges different approaches to Bell non-locality

Abstract

Bell's inequality fundamentally changed our understanding of quantum mechanics. Bell's insight that non-local correlations between quantum systems cannot be explained classically can be verified experimentally, and has numerous applications in modern quantum information. Today, the CHSH inequality is probably the most well-known Bell inequality and it has given us a wealth of understanding in what differentiates the classical from the quantum world. Yet, there are certainly other means of quantifying "Bell non-locality without inequalities" such as the famous Hardy's paradox. As such, one may wonder whether these are entirely different approaches to non-locality. For this anniversary issue, we unify the perspective of the CHSH inequality and Hardy Paradox into one family of non-local games which include both as special cases.