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Entanglement Dynamics and Classical Complexity.

Jiaozi Wang1, Barbara Dietz2, Dario Rosa2,3

  • 1Department of Physics, University of Osnabrück, D-49069 Osnabrück, Germany.

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|January 21, 2023
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Summary
This summary is machine-generated.

We found that the rate of entanglement growth in quantum systems can be predicted by classical dynamics. This rate is directly linked to the Kolmogorov-Sinai entropy, a measure of classical complexity.

Keywords:
quantum complexityquantum to classical transition

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Area of Science:

  • Quantum mechanics
  • Classical dynamics
  • Statistical physics

Background:

  • Studying the dynamical generation of entanglement in quantum systems is crucial for understanding quantum information processing.
  • A key challenge is to connect quantum phenomena with classical dynamics, especially in the quasiclassical regime.

Purpose of the Study:

  • To analytically investigate the dynamical generation of entanglement in a two-body interacting system.
  • To establish a direct link between the entanglement growth rate and classical dynamical complexity in the quasiclassical regime.

Main Methods:

  • Analytical derivation of entanglement growth rate from a separable coherent state.
  • Utilizing the Kolmogorov-Sinai entropy as a measure of classical complexity.
  • Numerical simulations on a model of coupled rotators for validation.

Main Results:

  • The entanglement growth rate in the quasiclassical regime can be computed from the underlying classical dynamics.
  • This rate is precisely given by the Kolmogorov-Sinai entropy.
  • Numerical simulations confirm the analytical findings for the coupled rotators model.

Conclusions:

  • A direct relationship is established between quantum entanglement generation and classical complexity in the quasiclassical regime.
  • The Kolmogorov-Sinai entropy serves as a quantitative predictor for entanglement growth rates.
  • This work bridges quantum phenomena with classical dynamical measures, offering insights into complex systems.