Nonlocality of Quantum States can be Transitive

[2412.10505] Nonlocality of Quantum States can be Transitive Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Quantum Physics arXiv:2412.10505 (quant-ph) [Submitted on 13 Dec 2024 ( v1 ), last revised 9 Apr 2026 (this version, v3)] 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 View a PDF of the paper titled Nonlocality of Quantum States can be Transitive, by Kai-Siang Chen and 4 other authors View PDF HTML (experimental) Abstract: As a striking manifestation of quantum entanglement, nonlocality has long played a pivotal role in shaping our understanding of the quantum world. When considering a Bell test involving three parties, we may even find a remarkable situation where the nonlocality in two bipartite subsystems {\em forces} the remaining bipartite subsystem to exhibit nonlocality. This intriguing effect, dubbed nonlocality transitivity, was first identified in the non-quantum non-signaling world in 2011. However, whether such transitivity could manifest within quantum theory has remained unresolved -- until now. Here, we provide the first affirmative answer to this open problem at the level of quantum states, thereby showing that there exists a quantum-realizable notion of nonlocality transitivity. Specifically, by 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 induces nonlocality in the remaining bipartite subsystem. En route to showing this, we also prove that multiple copies of the $W$-state marginals uniquely determine the global compatible state, thus establishing another instance when the parts determine the whole. Surprisingly, the nonlocality transitivity of quantum states also occurs among the reduced states of Haar-random three-qutrit pure states. We further show that the transitivity of quantum steering can already be demonstrated with the marginals of a three-qubit $W$ state, showing again another noteworthy difference between the two forms of quantum correlations. Finally, we present a simple method to construct quantum states and correlations that are nonlocal in all their non-unipartite marginals, which may be of independent interest. Comments: Please see the published open-access version for the final paper; v2: Substantially rewritten to improve clarity, and with various new results added; v1: 8+ pages, 1 figure; this is Ref. [86] of arXiv:2202.03523 Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2412.10505 [quant-ph] (or arXiv:2412.10505v3 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2412.10505 Focus to learn more arXiv-issued DOI via DataCite Journal reference: npj Quantum Inf 12, 37 (2026) Related DOI : https://doi.org/10.1038/s41534-025-01173-z Focus to learn more DOI(s) linking to related resources Submission history From: Kai-Siang Chen [ view email ] [v1] Fri, 13 Dec 2024 19:00:12 UTC (24 KB) [v2] Wed, 28 May 2025 02:14:22 UTC (417 KB) [v3] Thu, 9 Apr 2026 03:56:56 UTC (418 KB) Full-text links: Access Paper: View a PDF of the paper titled Nonlocality of Quantum States can be Transitive, by Kai-Siang Chen and 4 other authors View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2024-12 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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