Mixed-State Phases from Local Reversibility
5 affiliations
- 1Perimeter Institute for Theoretical Physics
- 2Stanford University
- 3University of Waterloo
- 4University of Pittsburgh
- 5University of California at San Diego
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.
Related
- Measures of Chirality in Mixed-State Topological Phases
- Mixed-state phases induced by power-law quantum channels
- Topological phases of bosons with local parity coupling on a dimerized lattice
- Lifting the mixed to the pure: quantum phases of matter from canonical purification
- Topological Mixed States: Phases of Matter from Axiomatic Approaches
BibTeX
@article{sang2026mixedstate,
title = {{Mixed-State Phases from Local Reversibility}},
author = {Shengqi Sang and Leonardo A. Lessa and Roger S. K. Mong and Tarun Grover and Chong Wang and Timothy H. Hsieh},
journal = {Physical Review X},
year = {2026},
month = aug,
doi = {10.1103/1kr5-jlcb},
url = {https://doi.org/10.1103/1kr5-jlcb},
note = {CC BY},
}
RIS
TY - JOUR
TI - Mixed-State Phases from Local Reversibility
AU - Shengqi Sang
AU - Leonardo A. Lessa
AU - Roger S. K. Mong
AU - Tarun Grover
AU - Chong Wang
AU - Timothy H. Hsieh
PY - 2026
DA - 2026/08/19
JO - Physical Review X
DO - 10.1103/1kr5-jlcb
UR - https://doi.org/10.1103/1kr5-jlcb
AB - 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.
SN - 2160-3308
ER -