Toric code decodability under coherent X/Z errors is dual to Majorana monitored dynamics whose symmetry class (D or DIII) dictates whether the generic transition is a measurement-induced entanglement transition or a topological transition between area-law phases.
Quan- tum criticality under decoherence or weak measurement,
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Decohered non-Abelian Kitaev quantum double states exhibit strong-to-weak spontaneous symmetry breaking of non-invertible higher-form symmetries and form an information convex set whose dimension equals the pure-state ground-state degeneracy.
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Decoding coherent errors in toric codes on honeycomb and square lattices: duality to Majorana monitored dynamics and symmetry classes
Toric code decodability under coherent X/Z errors is dual to Majorana monitored dynamics whose symmetry class (D or DIII) dictates whether the generic transition is a measurement-induced entanglement transition or a topological transition between area-law phases.
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Strong-to-weak spontaneous symmetry breaking of higher-form non-invertible symmetries in Kitaev's quantum double model
Decohered non-Abelian Kitaev quantum double states exhibit strong-to-weak spontaneous symmetry breaking of non-invertible higher-form symmetries and form an information convex set whose dimension equals the pure-state ground-state degeneracy.