General Hardy-Type Paradox Based on Bell inequality and its Experimental Test

TL;DR

This paper develops a general Hardy-type paradox framework based on Bell inequalities, introduces stronger paradoxes with higher success probabilities, and experimentally verifies these predictions in a two-qubit system.

Contribution

It presents a unified framework for Hardy-type paradoxes, identifies stronger variants with higher success rates, and experimentally confirms the theoretical results.

Findings

Stronger Hardy-type paradoxes have about four times higher success probability.

The GHZ paradox is shown as a special Hardy-type paradox.

Experimental results agree with theoretical predictions within errors.

Abstract

Local realistic models cannot completely describe all predictions of quantum mechanics. This is known as Bell's theorem that can be revealed either by violations of Bell inequality, or all-versus-nothing proof of nonlocality. Hardy's paradox is an important all-versus-nothing proof and is considered as "the simplest form of Bell's theorem". In this work, we theoretically build the general framework of Hardy-type paradox based on Bell inequality. Previous Hardy's paradoxes have been found to be special cases within the framework. Stronger Hardy-type paradox has been found even for the two-qubit two-setting case, and the corresponding successful probability is about four times larger than the original one, thus providing a more friendly test for experiment. We also find that GHZ paradox can be viewed as a perfect Hardy-type paradox. Meanwhile, we experimentally test the stronger Hardy-type paradoxes in a two-qubit system. Within the experimental errors, the experimental results coincide with the theoretical predictions.