Bridging the gap between classical and quantum many-body information dynamics

Abstract

The fundamental question of how information spreads in closed quantum many-body systems is often addressed through the lens of the bipartite entanglement entropy, a quantity that describes correlations in a comprehensive (nonlocal) way. Among the most striking features of the entanglement entropy are its unbounded linear growth in the thermodynamic limit, its asymptotic extensivity in finite-size systems, and the possibility of measurement-induced phase transitions, all of which have no obvious classical counterpart. Here, we show how these key qualitative features emerge naturally also in classical information spreading, as long as one treats the classical many-body problem on par with the quantum one, that is, by explicitly accounting for the exponentially large classical probability distribution. Our analysis is supported by extensive numerics on prototypical cellular automata and Hamiltonian systems, for which we focus on the classical mutual information and also introduce a `classical entanglement entropy'. Our study sheds light on the nature of information spreading in classical and quantum systems, and opens new avenues for quantum-inspired classical approaches across physics, information theory, and statistics.

arXiv comment15 pages, 7 figures

References in corpus (71)

• The density-matrix renormalization group in the age of matrix product states
• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• Quantum Simulation
• Nonequilibrium dynamics of closed interacting quantum systems
• Many-body localization, thermalization, and entanglement
• Entanglement entropy and conformal field theory
• Average Entropy of a Subsystem
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Unbounded growth of entanglement in models of many-body localization
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
• Operator Spreading in Random Unitary Circuits
• Measurement-Induced Phase Transitions in the Dynamics of Entanglement
• Area laws in quantum systems: mutual information and correlations
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Universal slow growth of entanglement in interacting strongly disordered systems
• Measurement-driven entanglement transition in hybrid quantum circuits
• Phase space representation of quantum dynamics
• Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
• Eigenstate Thermalization Hypothesis
• Quantum Simulators: Architectures and Opportunities
• Ballistic spreading of entanglement in a diffusive nonintegrable system
• Theory of the phase transition in random unitary circuits with measurements
• Measurement-induced criticality in random quantum circuits
• Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
• Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
• Critical properties of the measurement-induced transition in random quantum circuits
• The truncated Wigner method for Bose condensed gases: limits of validity and applications
• Entanglement Entropy dynamics in Heisenberg chains
• Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems
• Emergent statistical mechanics of entanglement in random unitary circuits
• Entanglement dynamics after quantum quenches in generic integrable systems
• Entanglement phase transitions in measurement-only dynamics
• Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory
• Many-Body Quantum Spin Dynamics with Monte Carlo Trajectories on a Discrete Phase Space
• Entanglement spreading in a minimal model of maximal many-body quantum chaos
• Measurement-induced phase transition: A case study in the non-integrable model by density-matrix renormalization group calculations
• Velocity-dependent Lyapunov exponents in many-body quantum, semi-classical, and classical chaos
• Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
• Non-equilibrium Gross-Pitaevskii dynamics of boson lattice models
• Quantum corrections to the dynamics of interacting bosons: beyond the truncated Wigner approximation
• Fractal, logarithmic and volume-law entangled non-thermal steady states via spacetime duality
• Exact thermalization dynamics in the "Rule 54" Quantum Cellular Automaton
• Anomalous Subdiffusion from Subsystem Symmetries
• Energy transport in disordered classical spin chains
• Bridging entanglement dynamics and chaos in semiclassical systems
• Entanglement dynamics in quantum many-body systems
• Asymptotic Prethermalization in Periodically Driven Classical Spin Chains
• Classical Prethermal Phases of Matter
• Light-cone spreading of perturbations and the butterfly effect in a classical spin chain
• Entanglement dynamics in Rule 54: Exact results and quasiparticle picture
• Floquet prethermalization in periodically driven classical spin systems
• Rule 54: Exactly solvable model of nonequilibrium statistical mechanics
• Floquet Phases of Matter via Classical Prethermalization
• Temperature dependence of butterfly effect in a classical many-body system
• Classical many-body chaos with and without quasiparticles
• Classical approaches to prethermal discrete time crystals in one, two, and three dimensions
• Characterizations of prethermal states in periodically driven many-body systems with unbounded chaotic diffusion
• Chronotopic Lyapunov Analysis: (I) a Comprehensive Characterization of 1D Systems
• Entanglement and the Sign Structure of Quantum States
• Stability and pre-thermalization in chains of classical kicked rotors
• Measurement-induced phase transition in a classical, chaotic many-body system
• Anomalous Dynamics and Equilibration in the Classical Heisenberg Chain
• Arresting classical many-body chaos by kinetic constraints
• Butterfly Effect and Spatial Structure of Information Spreading in a Chaotic Cellular Automaton
• Fermions as generalized Ising models
• Transport, correlations, and chaos in a classical disordered anharmonic chain
• Exact solution of the Rule 150 reversible cellular automaton

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• Measurement-induced phase transitions in $(d+1)$-dimensional stabilizer circuits
• Controlling entanglement at absorbing state phase transitions in random circuits
• Coherence requirements for quantum communication from hybrid circuit dynamics
• Purification Timescales in Monitored Fermions
• Triviality of quantum trajectories close to a directed percolation transition
• Entanglement Transitions in Unitary Circuit Games
• Scrambling in quantum cellular automata
• Generalizing measurement-induced phase transitions to information exchange symmetry breaking
• Quantum and Classical Dynamics with Random Permutation Circuits
• Entanglement transitions induced by quantum-data collection
• Measurement-Induced Phase Transitions in Informational Active Matter
• Measurement-Induced Phase Transition in State Estimation of Chaotic Systems and the Directed Polymer
• Prethermalization in periodically-driven nonreciprocal many-body spin systems
• Monitored Fluctuating Hydrodynamics
• Entanglement dynamics and Page curves in random permutation circuits
• Random Permutation Circuits Beyond Qubits are Quantum Chaotic
• Bridging Classical and Quantum Information Scrambling with the Operator Entanglement Spectrum