https://doi.org/10.1140/epjp/s13360-026-07532-9
Regular Article
Measurement-dependent nonlocality in tree tensor networks
1
School of Mathematics and Statistics, Shanxi University, 030006, Taiyuan, P. R. China
2
College of Mathematics, Taiyuan University of Technology, 030024, Taiyuan, P. R. China
3
School of Mathematics and Information Technology, Yuncheng University, 044000, Yuncheng, P. R. China
4
Key Laboratory of Complex Systems and Data Science of Ministry of Education, Shanxi University, 030006, Taiyuan, Shanxi, China
a
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Received:
8
February
2026
Accepted:
2
March
2026
Published online:
20
April
2026
Abstract
Bell inequalities of local reality and network local reality are established based on the assumption of measurement independence. The violation of Bell’s inequalities witnesses the existence of nonlocal correlations. However, the assumption of measurement independence is contradictory to a fully causal hidden variable theory. In this paper, we focus on measurement-dependent nonlocality in tree tensor networks. We derive corresponding measurement-dependent network locality inequalities, and investigate the degree of measurement independence required for signal-free classical local models to simulate nonlocal correlations under conditions where different parties exhibit measurement dependence. Our research findings indicate that, when both the first and last layers exhibit measurement dependence, the required degree of measurement independence is higher than in the scenario where only the last layer exhibits measurement dependence. This suggests that the former configuration offers greater security for applications in quantum communication. Furthermore, the number of input measurements has a significant impact on the measurement independence required for signal-free classical local models to simulate nonlocal correlations.
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All authors have contributed equally for this study.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
