Hardy's Paradox for High-Dimensional Systems: Beyond Hardy's Limit

TL;DR

This paper presents a new, simple proof of quantum nonlocality for high-dimensional systems that generalizes Hardy's paradox, showing increased nonlocal event probabilities with system dimension and equivalence to Bell inequality violations.

Contribution

The authors introduce a simple, generalized proof of nonlocality that extends Hardy's paradox to high-dimensional systems and links it to Bell inequality violations.

Findings

Nonlocal event probability increases with system dimension

Proof encompasses Hardy's paradox as a special case

Equivalent to violation of a tight Bell inequality

Abstract

Hardy's proof is considered the simplest proof of nonlocality. Here we introduce an equally simple proof that (i) has Hardy's as a particular case, (ii) shows that the probability of nonlocal events grows with the dimension of the local systems, and (iii) is always equivalent to the violation of a tight Bell inequality.