Symmetry Properties of Quantum Dynamical Entropy
arXiv:2502.04442 · doi:10.1103/5slc-qj5n
Abstract
As quantum analogs of the classical Kolmogorov-Sinai entropy, quantum dynamical entropies have emerged as important tools to characterize complex quantum dynamics. In particular, Alicki-Fannes-Lindblad (AFL) entropy, which quantifies the information production rate of a coherent quantum system subjected to repeated measurement, has received considerable attention as a potential diagnostic for quantum chaos. Despite this interest, the precise behavior of quantum dynamical entropy in the presence of symmetry remains largely unexplored. In this work, we establish rigorous inequalities of the AFL entropy for arbitrary unitary dynamics (single-particle and many-body) in the presence of various types of symmetry. Our theorems encompass three cases: Abelian symmetry, an anticommuting unitary, and non-Abelian symmetries. In particular, we show that, while the cumulative AFL entropy generally saturates to the dimensional bound at late times for chaotic dynamics, this saturation value is distinctively lower when the measurements respect the symmetries. We motivate our main results with numerical simulations of the perturbed quantum cat maps. Our findings highlight the crucial role of symmetry in quantum dynamics under measurements, and our framework is readily adaptable for investigating symmetry's influence across diverse probes of quantum chaos.
Accepted to Physical Review A. 13+6 pages, 2 columns, 11 figures
References in corpus (71)
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Many-body localization, thermalization, and entanglement
- Measurement-Induced Phase Transitions in the Dynamics of Entanglement
- Quantum Zeno Effect and the Many-body Entanglement Transition
- Chaos in quantum channels
- Random Quantum Circuits
- Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks
- The Ryu-Takayanagi Formula from Quantum Error Correction
- A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
- Symmetry-resolved entanglement in many-body systems
- Chaos, Complexity, and Random Matrices
- Many-body quantum chaos: Analytic connection to random matrix theory
- The Eigenstate Thermalization Hypothesis and Out of Time Order Correlators
- Chaos signatures in the short and long time behavior of the out-of-time ordered correlator
- Timelike entanglement entropy
- Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial
- Exact emergent quantum state designs from quantum chaotic dynamics
- Gauging classical and quantum integrability through out-of-time ordered correlators
- Dynamical purification and the emergence of quantum state designs from the projected ensemble
- Eigenstate Correlations, Thermalization and the Butterfly Effect
- Pseudo Entropy in Free Quantum Field Theories
- Solvable model of deep thermalization with distinct design times
- Scrambling is Necessary but Not Sufficient for Chaos
- Aspects of Pseudo Entropy in Field Theories
- Superdensity Operators for Spacetime Quantum Mechanics
- A Noisy Approach to Intrinsically Mixed-State Topological Order
- Out-of-time-order correlations and the fine structure of eigenstate thermalisation
- Non-Abelian eigenstate thermalization hypothesis
- On holographic time-like entanglement entropy
- Island for Gravitationally Prepared State and Pseudo Entanglement Wedge
- EPR Pairs, Local Projections and Quantum Teleportation in Holography
- A Maximum Entropy Principle in Deep Thermalization and in Hilbert-Space Ergodicity
- Quantum Lyapunov Spectrum
- Operator Spreading in Quantum Maps
- Characterizing complexity of many-body quantum dynamics by higher-order eigenstate thermalization
- Signature of quantum chaos in operator entanglement in 2d CFTs
- Topological pseudo entropy
- From Symmetries to Commutant Algebras in Standard Hamiltonians
- Holographic measurement and bulk teleportation
- Classical decays in decoherent quantum maps
- Constructible reality condition of pseudo entropy via pseudo-Hermiticity
- Quantum chaos in a system with high degree of symmetries
- Spectral properties of noisy classical and quantum propagators
- Geometric Interpretation of Timelike Entanglement Entropy
- QUANTIZATION OF A CLASS OF PIECEWISE AFFINE TRANSFORMATIONS ON THE TORUS
- Dynamical quantum ergodicity from energy level statistics
- Deep thermalization in constrained quantum systems
- Spectral properties and classical decays in quantum open systems
- Information Scrambling with Conservation Laws
- Classical bifurcations and entanglement in smooth Hamiltonian system
- Operational Metric for Quantum Chaos and the Corresponding Spatiotemporal Entanglement Structure
- Quantum dynamical entropy and decoherence rate
- Momentum dependent quantum Ruelle-Pollicott resonances in translationally invariant many-body systems
- Robustness of quantum chaos and anomalous relaxation in open quantum circuits
- Relaxation of Multitime Statistics in Quantum Systems
- Symmetry enforced entanglement in maximally mixed states
- Holographic measurement in CFT thermofield doubles
- Entropy rate of message sources driven by quantum walks
- Entangling power of baker's map: Role of symmetries
- Classical Limit of Quantum Dynamical Entropies
- Information-theoretical meaning of quantum dynamical entropy
- Highly entangled stationary states from strong symmetries
- Quantum dynamical entropy, chaotic unitaries and complex Hadamard matrices
- The quantum cat map on the modular discretization of extremal black hole horizons
- Non-abelian symmetry-resolved entanglement entropy
- Spectral Approach to Chaos and Quantum-Classical Correspondence in Quantum Mapas
- Quantum Kolmogorov-Sinai entropy and Pesin relation
- Quantum-classical correspondence on compact phase space
- Egorov property in perturbed cat map
- Holographic Kolmogorov-Sinai entropy and the quantum Lyapunov spectrum
- Quantum dynamical entropies for classical stochastic systems