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  • Open Access

Mixed-State Phases from Local Reversibility

Shengqi Sang1,2,*,**, Leonardo A. Lessa2,3,†,**, Roger S. K. Mong4,‡, Tarun Grover5,§, Chong Wang2,∥, and Timothy H. Hsieh2,¶

  • *Contact author: sangsq@stanford.edu
  • †Contact author: llessa@pitp.ca
  • ‡Contact author: rmong@pitt.edu
  • §Contact author: tagrover@ucsd.edu
  • ∥Contact author: cwang4@pitp.ca
  • Contact author: thsieh@pitp.ca
  • **These authors contributed equally to this work.
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Phys. Rev. X 16, 041014 – Published 13 October, 2026

DOI: https://doi.org/10.1103/1kr5-jlcb

Abstract

We propose a refined definition of mixed-state phase equivalence based on locally reversible channel circuits. We show that such circuits preserve topological degeneracy and the locality of all operators including both strong and weak symmetries. Under a locally reversible channel, weak unitary symmetries are locally dressed into channel symmetries, a generalization of symmetry for open quantum systems. For Abelian higher-form symmetries, we show the refined definition preserves anomalies and spontaneous breaking of such symmetries within a phase. As a primary example, a two-dimensional classical loop ensemble is trivial under the previously adopted definition of mixed-state phases. However, it has nontrivial topological degeneracy arising from a mutual anomaly between strong and weak 1-form symmetries, and our results show that it is not connected to a trivial state via locally reversible channel circuits.

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Popular Summary

Classifying and characterizing phases of matter is a central endeavor in many-body physics. Extending the conventional circuit-based definition of pure-state phases to mixed states has proved subtle, as existing criteria can classify a state as trivial even when it exhibits nontrivial behavior such as robust information storage. To resolve this, we propose a refined framework based on local reversibility, requiring every step of a transformation circuit to be locally undoable. We demonstrate that transformations satisfying this condition preserve long-range properties, including topological degeneracy and symmetry anomalies. Applied to the two-dimensional classical loop model, our framework successfully identifies a nontrivial phase that earlier definitions classify as trivial. This work establishes a firm foundation for classifying and understanding the phases of noisy, thermal, and dissipative many-body systems.

Article Text

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Phys. Rev. X 16, 041014– Published 13 October, 2026
  • Received 19 January 2026
  • Revised 19 June 2026
  • Accepted 19 August 2026
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