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Entangling power of quantized chaotic systems.

A Lakshminarayan1

  • 1Physical Research Laboratory, Navrangpura, Ahmedabad 380 009, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 3, 2001
PubMed
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Classical chaos significantly boosts quantum entanglement in quantum systems. This enhanced entanglement aids in characterizing complex quantum states and reveals insights into wave-function localization.

Area of Science:

  • Quantum mechanics
  • Chaos theory
  • Quantum information

Background:

  • Quantum entanglement is a key resource in quantum information.
  • Understanding entanglement in chaotic systems is crucial for quantum computing and complex system analysis.
  • Classical-to-quantum transitions in chaotic systems remain an active research area.

Purpose of the Study:

  • To investigate the relationship between classical chaos and quantum entanglement.
  • To explore entanglement in both eigenstates and time-evolving states.
  • To utilize entanglement as a tool for characterizing quantum states in chaotic systems.

Main Methods:

  • Calculating von Neumann entropy of reduced density matrices.
  • Analyzing entanglement in eigenstates and time-evolving states.

Related Experiment Videos

  • Connecting eigenfunction localization with Schmidt vectors and eigenvalues.

    • Main Results:

    • Classical chaos substantially enhances quantum entanglement.
    • Entanglement serves as a robust characterization for quantum states in higher-dimensional chaotic systems.
    • Eigenfunction localization information is graded within Schmidt vectors, with scarring by classical periodic orbits.
    • Reduced density matrix eigenvalues show exponential arrangement and sensitivity to localization.

    Conclusions:

    • Classical chaos is a powerful driver of quantum entanglement.
    • Entanglement provides a valuable lens for understanding complex quantum systems.
    • The study reveals deep connections between classical dynamics, quantum entanglement, and wave-function properties.