Three-qubit nonlocality paradoxes: beyond GHZ
Abstract
Quantum nonlocality paradoxes, such as that of GHZ, provide maximally sharp logical obstructions to classical probabilistic models of quantum correlations. They are key resources in a broad variety of information-theoretic tasks that exhibit unconditional quantum advantage. For example, in nonlocal games, which are communication tasks that serve as core technical tools in recent landmark results in quantum computational complexity theory. Their role in establishing quantum advantage motivated their study by Abramsky et al. who introduced an infinite family of three-qubit paradoxes exhibiting novel conditional structure. This was later extended by the present authors into a full classification program. In this work, we completely classify all three-qubit nonlocality paradoxes established via a biconditional parity proof; this is a very large class of paradoxes that encompasses all earlier-known examples. We do this by introducing a suite of new structural and combinatorial techniques. We find that the landscape of nonlocality paradoxes is far richer than previously understood, violating regularity conditions underlying all prior constructions.
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BibTeX
@misc{silva2026threequbit,
title = {{Three-qubit nonlocality paradoxes: beyond GHZ}},
author = {Nadish de Silva and Santanil Jana and Ming Yin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.00795},
eprint = {2607.00795},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.00795},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Three-qubit nonlocality paradoxes: beyond GHZ
AU - Nadish de Silva
AU - Santanil Jana
AU - Ming Yin
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2607.00795
UR - https://arxiv.org/abs/2607.00795
AB - Quantum nonlocality paradoxes, such as that of GHZ, provide maximally sharp logical obstructions to classical probabilistic models of quantum correlations. They are key resources in a broad variety of information-theoretic tasks that exhibit unconditional quantum advantage. For example, in nonlocal games, which are communication tasks that serve as core technical tools in recent landmark results in quantum computational complexity theory. Their role in establishing quantum advantage motivated their study by Abramsky et al. who introduced an infinite family of three-qubit paradoxes exhibiting novel conditional structure. This was later extended by the present authors into a full classification program. In this work, we completely classify all three-qubit nonlocality paradoxes established via a biconditional parity proof; this is a very large class of paradoxes that encompasses all earlier-known examples. We do this by introducing a suite of new structural and combinatorial techniques. We find that the landscape of nonlocality paradoxes is far richer than previously understood, violating regularity conditions underlying all prior constructions.
ER -