Fate of average symmetry-protected topological states under symmetry-preserving quantum operations

arXiv:2609.27530 · quant-ph, cond-mat.stat-mech, cond-mat.str-el · Submitted 2026-09-23 · Read on arXiv

quant-ph, cond-mat.stat-mech, cond-mat.str-el

Submitted: 2026-09-23

Updated: 2026-09-23

Terminology

• Effective Hamiltonian — 14× in this paper · explained in 2 episodes
• Hilbert Space — 8× in this paper · explained in 2 episodes
• Robustness — 5× in this paper · explained in 5 episodes
• Entanglement — 4× in this paper · explained in 4 episodes
• Entanglement Entropy — 4× in this paper · explained in 2 episodes
• Symmetry Breaking — 4× in this paper · explained in 3 episodes
• Phase Transitions — 2× in this paper · explained in 2 episodes
• Trace — 2× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Topological Order — 1× in this paper · explained in 2 episodes

Sources

• Tensor network formulation of symmetry protected topological phases in mixed states
• Mixed-state topological order and the errorfield double formulation of decoherence-induced transitions
• Measurement-based quantum computation
• Strong-to-Weak Symmetry Breaking Phases in Steady States of Quantum Operations
• Mixed-state long-range order and criticality from measurement and feedback
• Nonequilibrium topological response under charge dephasing
• Hierarchy of mixed symmetry protected topological states in extended cluster states under subsystem decoherence
• Lecture Notes on the Theory of Open Quantum Systems

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