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  • Open Access

Vanishing correlations in stochastic and bistochastic controlled circuits

Pavel Kos1,2,*, Bruno Bertini3, and Tomaž Prosen1

  • *Contact author: pavel.kos@fmf.uni-lj.si
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Phys. Rev. E 113, 064139 – Published 18 June, 2026

DOI: https://doi.org/10.1103/4rn3-bn7k

Abstract

We study the dynamics of circuits composed of stochastic and bistochastic controlled gates. This type of dynamics arises from quantum circuits with random controlled gates, as well as in stochastic circuits and deterministic classical cellular automata. We prove that stochastic and bistochastic controlled gates lead to two-point spatiotemporal correlation functions that vanish everywhere except when the two operators act on the same site. More generally, for multipoint correlations the two rightmost operators must act on the same site. We argue that autocorrelation, while hard to compute, typically decays exponentially toward a value that is exponentially small in the system size. Our results reveal a broad class of quantum systems that exhibit surprisingly simple correlation structures despite their complex microscopic dynamics.

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Phys. Rev. E 113, 064139– Published 18 June, 2026
  • Received 26 January 2026
  • Accepted 21 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. Open access publication funded by Max Planck Society.

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