Locally reversible channel circuits define a refined mixed-state phase equivalence under which the 2D classical loop ensemble is non-trivially ordered, with topological degeneracy protected.
IV that the spontaneous symme- try breaking of 1-form symmetries, or equivalently the ’t Hooft anomaly associated with the symmetries, is also a phase invariant
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Mixed-state phases from local reversibility
Locally reversible channel circuits define a refined mixed-state phase equivalence under which the 2D classical loop ensemble is non-trivially ordered, with topological degeneracy protected.