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arXiv · 2601.01445

A Logical Formalism of Hardy-type Paradox

Songyi Liu·Yongjun Wang·Baoshan Wang·Chang He·Yunyi Jia
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Abstract

Hardy-type paradoxes provide elegant, inequality-free proofs of quantum contextuality. We introduce a unified logical formalism for these paradoxes, termed logical Hardy-type paradoxes. For any finite quantum scenario of ideal measurements, we prove that the existence of a logical Hardy-type paradox is equivalent to logical contextuality. Specifically, strong contextuality is equivalent to logical Hardy-type paradoxes with success probability SP = 1. These results generalize prior work on (2,k,2), (2,2,d), and n-cycle scenarios. We analyze logical Hardy-type paradoxes in the Mansfield and Klyachko-Can-Binicioglu-Shumovsky (KCBS) scenarios. In the KCBS scenario, we show that there is exactly one type of logical Hardy-type paradox, achieving SP\approx 10.56% for a specific parameter setting.

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Songyi Liu, Yongjun Wang, Baoshan Wang, Chang He, Yunyi Jia. 2026-01-04. A Logical Formalism of Hardy-type Paradox. https://arxiv.org/abs/2601.01445

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