Measurement-induced Lévy flights of quantum information

Abstract

We explore a model of free fermions in one dimension, subject to frustrated (non-commuting) local measurements across adjacent sites, which resolves the fermions into non-orthogonal 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 $S\propto {\ell }^{1/3}$ for a subsystem of length $\ell$. We derive an effective non-linear 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 $\ell$, consecutive regimes of superdiffusive, $S\propto {\ell }^{1/3}$, diffusive, $S\propto \ln \ell$, and localized, $S=\mathrm{const}$, behavior. Our findings show how intricate fractal-scaling entanglement can be produced for local Hamiltonians and measurements.

7+15 pages, 8 figures

References in corpus (1)

• Quantum Noise as an Entanglement Meter

Cited by in corpus (7)

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• Measurement-Induced Phase Transition in a Disordered XX Spin Chain: A Real-Space Renormalization Group Study
• Controlled Zeno-Induced Localization of Free Fermions in a Quasiperiodic Chain
• Generation of Volume-Law Entanglement by Local-Measurement-Only Quantum Dynamics