Strong-to-weak spontaneous symmetry breaking of higher-form non-invertible symmetries in Kitaev's quantum double model

arXiv:2509.24179 · quant-ph · Submitted 2025-09-29 · Read on arXiv

quant-ph

Submitted: 2025-09-29

Updated: 2026-09-20

Terminology

• Anyons — 21× in this paper · explained in 2 episodes
• Symmetry Breaking — 13× in this paper · explained in 3 episodes
• Topological Order — 12× in this paper · explained in 2 episodes
• Degeneracy — 6× in this paper · explained in 3 episodes
• Entanglement — 4× in this paper · explained in 4 episodes
• Holonomy — 4× in this paper · explained in 2 episodes
• Trace — 2× in this paper · explained in 2 episodes
• Anyon Condensation — 1× in this paper · explained in 1 episode
• Domain Walls — 1× in this paper · explained in 2 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Multipartite Entanglement — 1× in this paper · explained in 2 episodes
• Phase Transitions — 1× in this paper · explained in 2 episodes

Sources

• A modular functor which is universal for quantum computation
• Topological quantum memory
• ICTP Lectures on (Non-)Invertible Generalized Symmetries
• What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries
• Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases
• Fusion Category Symmetry II: Categoriosities at c = 1 and Beyond
• Diagnostics of mixed-state topological order and breakdown of quantum memory
• Symmetry protected topological phases under decoherence
• Fidelity Strange Correlators for Average Symmetry-Protected Topological Phases
• Symmetry Protected Topological Phases of Mixed States in the Doubled Space
• Tensor network formulation of symmetry protected topological phases in mixed states
• Locally Purified Density Operators for Symmetry-Protected Topological Phases in Mixed States
• Designing open quantum systems with known steady states: Davies generators and beyond
• Symmetry-enforced many-body separability transitions
• Separability transitions in topological states induced by local decoherence
• Unconventional topological mixed-state transition and critical phase induced by self-dual coherent errors
• Mixed-state quantum anomaly and multipartite entanglement
• Intrinsic Mixed-state Topological Order
• Anomaly in open quantum systems and its implications on mixed-state quantum phases
• Spontaneous Strong Symmetry Breaking in Open Systems: Purification Perspective

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