Hardy's paradox is of fundamental importance in quantum information theory. So far, there have been two types of its extensions into higher dimensions: in the first type the maximum probability of nonlocal events is roughly 9% and remains the same as the dimension changes (dimension-independent), while in the second type the probability becomes larger as the dimension increases, reaching approximately 40% in the infinite limit. Here, we (i) give an alternative proof of the first type, (ii) study the situation in which the maximum probability of nonlocal events can also be dimension-independent in the second type, and (iii) conjecture how the situation could be changed in order that (ii) still holds.
@article{arxiv.1406.5812,
title = {Dimension-Independent Bounds for Hardy's Experiment},
author = {Zhen-Peng Xu and Hong-Yi Su and Jing-Ling Chen},
journal= {arXiv preprint arXiv:1406.5812},
year = {2015}
}