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Measurement-Induced Lévy Flights of Quantum Information

Igor Poboiko1,2,*, Marcin Szyniszewski3,4,*, Christopher J. Turner3, Igor V. Gornyi1,2, Alexander D. Mirlin1,2, and Arijeet Pal3

  • *These authors contributed equally to this work.
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Phys. Rev. Lett. 135, 170403 – Published 21 October, 2025

DOI: https://doi.org/10.1103/tx71-1cd9

Abstract

We explore a model of free fermions in one dimension, subject to frustrated (noncommuting) local measurements across adjacent sites, which resolves the fermions into nonorthogonal orbitals, misaligned from the underlying lattice. For maximal misalignment, superdiffusive behavior emerges from the vanishing of the measurement-induced quasiparticle decay rate at one point in the Brillouin zone, which generates fractal-scaling entanglement entropy S∝ℓ1/3 for a subsystem of length ℓ. We derive an effective nonlinear sigma model with long-range couplings responsible for Lévy flights in entanglement propagation, which we confirm with large-scale numerical simulations. When the misalignment is reduced, the entanglement exhibits, with increasing ℓ, consecutive regimes of superdiffusive, S∝ℓ1/3, diffusive, S∝lnℓ, and localized, S=const, behavior. Our findings show how intricate fractal-scaling entanglement can be produced for local Hamiltonians and measurements.

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Phys. Rev. Lett. 135, 170403– Published 21 October, 2025
  • Received 22 January 2025
  • Revised 17 April 2025
  • Accepted 30 September 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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