Nonlocality of Quantum States can be Transitive

• URL: http://arxiv.org/abs/2412.10505v1
• Date: Fri, 13 Dec 2024 19:00:12 GMT
• Title: Nonlocality of Quantum States can be Transitive
• Authors: Kai-Siang Chen, Gelo Noel M. Tabia, Chung-Yun Hsieh, Yu-Chun Yin, Yeong-Cherng Liang,
• Abstract summary: We show that quantum steering already exhibits transitivity in a three-qubit setting. We also discuss connections between the problem of nonlocality transitivity and the largely overlooked polygamous nature of nonlocality.
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• Abstract: In a Bell test involving three parties, one may find a curious situation where the nonlocality in two bipartite subsystems forces the remaining bipartite subsystem to exhibit nonlocality. Post-quantum examples for this phenomenon, dubbed nonlocality transitivity, have been found in 2011. However, the question of whether nonlocality transitivity occurs within quantum theory has remained unresolved -- until now. Here, we provide the first affirmative answer to this question at the level of quantum states. Leveraging the possibility of Bell-inequality violation by tensoring, we analytically construct a pair of nonlocal bipartite states such that simultaneously realizing them in a tripartite system forces the remaining bipartite state to be nonlocal. En route to showing this, we prove that multiple copies of the $W$-state marginals uniquely determine the global compatible state. Furthermore, in contrast to Bell-nonlocality, we show that quantum steering already exhibits transitivity in a three-qubit setting, thus revealing another significant distinction between Bell-nonlocality and steering. We also discuss connections between the problem of nonlocality transitivity and the largely overlooked polygamous nature of nonlocality.

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