Realigned Hardy's Paradox

TL;DR

The paper introduces a realigned Hardy's paradox that significantly enhances Hardy violation, making experimental tests of quantum nonlocality more robust and feasible under practical imperfections.

Contribution

It proposes a new version of Hardy's paradox with higher violation and simpler structure, applicable to multiple measurement scenarios, improving robustness against experimental imperfections.

Findings

Achieves Hardy values of approximately 0.4140 for n=2 and 0.7734 for n=4.

Simplifies Hardy's paradox with only one condition instead of three.

Enhances tolerance to experimental imperfections.

Abstract

Hardy's paradox provides an all-versus-nothing fashion to directly certify that quantum mechanics cannot be completely described by local realistic theory. However, when considering potential imperfections in experiments, like imperfect entanglement source and low detection efficiency, the original Hardy's paradox may induce a rather small Hardy violation and only be realized by expensive quantum systems. To overcome this problem, we propose a realigned Hardy's paradox. Compared with the original version of Hardy's paradox, the realigned Hardy's paradox can dramatically improve the Hardy violation. Then, we generalize the realigned Hardy's paradox to arbitrary even $n$ dichotomic measurements. For $n=2$ and $n=4$ cases, the realigned Hardy's paradox can achieve Hardy values $P(00|A_1B_1)$ approximate $0.4140$ and $0.7734$ respectively compared with $0.09$ of the original Hardy's paradox. Meanwhile, the structure of the realigned Hardy's paradox is simpler and more robust in the sense that there is only one Hardy condition rather than three conditions. One can anticipate that the realigned Hardy's paradox can tolerate more experimental imperfections and stimulate more fascinating quantum information applications.