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Symmetry and Topology of Monitored Quantum Dynamics
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Symmetry and Topology of Monitored Quantum Dynamics
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The interplay between unitary dynamics and quantum measurements induces diverse phenomena in open quantum systems with no counterparts in closed quantum systems at equilibrium. Here, we generally classify Kraus operators and their effective non-Hermitian dynamical generators, thereby establishing the tenfold classification for symmetry and topology of monitored free fermions. Our classification elucidates the role of topology in measurement-induced phase transitions and identifies potential topological terms in the corresponding nonlinear sigma models. Furthermore, we establish the bulk-boundary correspondence in monitored quantum dynamics: nontrivial topology in spacetime manifests itself as topologically nontrivial steady states and gapless boundary states in Lyapunov spectra, such as Lyapunov zero modes and chiral edge modes, leading to the topologically protected slowdown of dynamical purification.
Forward citations
Cited by 7 Pith papers
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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 t...
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Free-Fermion Dynamics with Measurements: Topological Classification and Adaptive Preparation of Topological States
Symmetry classification of measurement-inclusive fermionic dynamics with equivalence between many-body and single-particle schemes, plus post-selection-free adaptive circuits for topological states in four classes.
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Replica Keldysh field theory of quantum-jump processes: General formalism and application to imbalanced and inefficient fermion counting
A replica Keldysh field theory for general quantum-jump processes is derived; for imbalanced and inefficient 1D fermion counting it predicts no measurement-induced transition and an inefficiency scale ξ∼(1−η)^{−1/2}, ...
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Absence of measurement- and unraveling-induced entanglement transitions in continuously monitored one-dimensional free fermions
Replica Keldysh analysis shows monitored 1D free fermions exhibit area-law entanglement beyond an exponentially large scale ln(l_φ,*) ~ J/[γ cos(φ)], with no genuine measurement- or unraveling-induced entanglement tra...
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Quantum dynamics of monitored free fermions: Evolution of quantum correlations and scaling at measurement-induced phase transition
Monitored free fermions are mapped to a nonlinear sigma model whose finite-time evolution and quasi-1D long-time scaling are used to locate the measurement-induced transition and extract the correlation-length exponen...
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Entanglement dynamics of monitored noninteracting fermions on graphics processing units
GPU-enabled simulations at L=16384 (1D) and 160x160 (2D) confirm no MIPT in 1D but a finite-rate MIPT in 2D with ν≈1.3, partially disagreeing with NLSM predictions.
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Noisy Monitored Quantum Circuits
A review showing that in noisy monitored quantum circuits, any noise enforces area-law entanglement with characteristic q^{-1/3} scaling and noise-correlation-dependent information-protection timescales.
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