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.

15 pages, 7 figures

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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