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Measurement-Induced Lévy Flights of Quantum Information
Igor Poboiko1,2, Marcin Szyniszewski3,4, Christopher J Turner3
1Karlsruhe Institute of Technology, Institute for Quantum Materials and Technologies, 76131 Karlsruhe, Germany.
Physical Review Letters
|November 7, 2025
Summary
Researchers studied frustrated measurements on one-dimensional free fermions, revealing fractal entanglement entropy S∝ℓ^{1/3} due to superdiffusive behavior. This work demonstrates complex fractal patterns from local quantum measurements.
Area of Science:
- Quantum physics
- Condensed matter physics
- Many-body systems
Background:
- Frustrated local measurements on one-dimensional free fermions lead to nonorthogonal orbitals.
- Understanding the emergence of complex entanglement patterns is crucial in quantum systems.
Purpose of the Study:
- To explore a model of free fermions under frustrated local measurements.
- To investigate the emergence of superdiffusive behavior and fractal entanglement entropy.
- To derive and confirm an effective nonlinear sigma model for entanglement propagation.
Main Methods:
- Theoretical modeling of one-dimensional free fermions with frustrated local measurements.
- Derivation of an effective nonlinear sigma model with long-range couplings.
- Large-scale numerical simulations to confirm theoretical predictions.
Main Results:
- Maximal misalignment leads to superdiffusive behavior and fractal entanglement entropy (S∝ℓ^{1/3}).
- A nonlinear sigma model explains Lévy flights in entanglement propagation.
- Reduced misalignment reveals consecutive regimes of superdiffusive, diffusive (S∝lnℓ), and localized (S=const) entanglement.
Conclusions:
- Intricate fractal-scaling entanglement can arise from local Hamiltonians and measurements.
- The study provides insights into the relationship between measurement, frustration, and entanglement in quantum systems.
- The findings highlight novel pathways to generate complex quantum states and phenomena.
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