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  • Open Access

Mixed-state learnability transitions in monitored noisy quantum dynamics

Hansveer Singh1,*, Romain Vasseur2, Andrew C. Potter3, and Sarang Gopalakrishnan4

  • *Contact author: hsingh@pks.mpg.de
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Phys. Rev. B 113, 054305 – Published 9 February, 2026

DOI: https://doi.org/10.1103/6b9y-scyz

Abstract

We consider learnability transitions in monitored quantum systems that undergo noisy evolution, subject to a global strong symmetry—i.e., in addition to the measuring apparatus, the system can interact with an unobserved environment, but does not exchange charge with it. As in the pure-state setting, we find two information-theoretic phases—a sharp (fuzzy) phase in which an eavesdropper can rapidly (slowly) learn the symmetry charge. However, because the dynamics is noisy, both phases can be simulated efficiently using tensor networks. Indeed, even when the true dynamics is unitary, introducing noise by hand allows an eavesdropper to efficiently learn the symmetry charge from local measurements, as we demonstrate. We identify the fuzzy phase in this setting as a mixed-state phase that exhibits spontaneous strong-to-weak symmetry breaking.

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Phys. Rev. B 113, 054305– Published 9 February, 2026
  • Received 15 September 2025
  • Revised 1 December 2025
  • Accepted 12 January 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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