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Temporal Entanglement Transition in Chaotic Quantum Many-Body Dynamics

Ilya Vilkoviskiy1,2, Michael Sonner2,3,4, Qi Camm Huang5, Wen Wei Ho5,6, Alessio Lerose2,7,8, and Dmitry A. Abanin1,9,10

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PRX Quantum 7, 043024 – Published 4 November, 2026

DOI: https://doi.org/10.1103/s39j-czpf

Abstract

Temporal entanglement (TE) of an influence matrix (IM) has been proposed as a measure of the complexity of simulating dynamics of local observables in many-body systems. Foligno et al. Phys. Rev. X 13, 041008 (2023) recently argued that the TE in chaotic 1D quantum circuits obeys linear (volume law) scaling with evolution time. To reconcile this apparent high complexity of IM with the rapid thermalization of local observables, here we study the relation between TE, non-Markovianity, and local temporal correlations for chaotic quantum baths. By exactly solving a random-unitary bath model and bounding distillable entanglement between future and past degrees of freedom, we identify a regime where TE is extensive and reflects genuine non-Markovianity. This memory, however, is entirely contained in highly complex temporal correlations, and its effect on few-point temporal correlators is negligible. An IM coarse-graining procedure, reducing the allowed frequency of measurements of the probe system, results in a transition from volume- to subvolume- (area or logarithmic) law TE scaling. We demonstrate the generality of this TE transition in 1D circuits by analyzing the kicked Ising model analytically at dual-unitary points, as well as numerically away from them. This finding indicates that dynamics of local observables are fully captured by a subvolume-law IM. We provide evidence that the compact IM MPS obtained via standard compression algorithms accurately describes local evolution.

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Popular Summary

Simulating a small part of a chaotic quantum system can be surprisingly hard, even when that part rapidly settles into thermal equilibrium. Influence matrices describe how the surrounding system affects a local probe, but their temporal entanglement—quantum correlations linking past and future—can grow linearly with time, making faithful simulations exponentially costly.

We show that this complexity reflects genuine non-Markovianity: the environment retains memory of its earlier interactions with the probe. Yet this memory is hidden in complicated correlations spanning many observation times, with little effect on simpler observables.

Remarkably, restricting how frequently the probe can be measured produces a sharp transition: temporal entanglement changes from linear growth to logarithmic or bounded growth. This coarse-graining preserves all correlations at the retained observation times exactly, while allowing much more compact descriptions. In chaotic periodically driven spin chains, compressed influence matrices accurately reproduce local relaxation, including unusually slow thermalization.

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PRX Quantum 7, 043024– Published 4 November, 2026
  • Received 30 November 2025
  • Revised 13 August 2026
  • Accepted 5 October 2026
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