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Latent splitting as a causal probe

Santiago Zamora1,2, Pedro Lauand3,4, Isadora Veeren5,6, Davide Poderini7, and Rafael Chaves1,8

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Phys. Rev. A 113, 062415 – Published 4 June, 2026

DOI: https://doi.org/10.1103/b1qw-sbw2

Abstract

Generalizations of Bell's framework to causal networks have yielded foundational insights and applications, including the use of interventions to enhance the detection of nonclassicality in scenarios with communication. Such interventions, however, become uninformative when all observable variables are space-like separated. To address this limitation, we introduce the latent splitting procedure, a generalization of interventions to quantum networks in which controlled manipulations are applied to latent quantum systems. We show that latent splitting enables the detection of nonclassicality by combining observational and interventional data even when conventional interventions fail. Focusing on the triangle network, we derive analytical witnesses that robustly certify nonclassicality, including nonlinear inequalities for minimal binary-variable scenarios and extensions of the nonclassical region of previously proposed experiments.

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Phys. Rev. A 113, 062415– Published 4 June, 2026
  • Received 11 February 2026
  • Accepted 14 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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