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

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.

arXiv commentTo appear in J Phys A: Math. Theor. Special Issue in the honor of the 50 year anniversary of Bell's theorem

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Cited by in corpus (8)

• Geometry of the set of quantum correlations
• The Inflation Technique for Causal Inference with Latent Variables
• Increased success probability in Hardy's nonlocality: Theory and demonstration
• Hardy's paradox as a demonstration of quantum irrealism
• Device-independent bounds from Cabello's nonlocality argument
• Nonlocal Position Changes of a Photon Revealed by Quantum Routers
• Quantum correlations on the no-signaling boundary: self-testing and more
• Non-local games and optimal steering at the boundary of the quantum set