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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

Summary

This summary is machine-generated.

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.

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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.
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.