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Entanglement and its relationship to classical dynamics.

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We analyzed the quantum kicked top, finding entanglement strongly depends on initial conditions, correlating with classical trajectory behavior, not just chaos. This quantum entanglement shows clear periodic patterns with kicks.

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Area of Science:

  • Quantum mechanics
  • Quantum chaos
  • Quantum information theory

Background:

  • The quantum kicked top is a model system for studying quantum chaos.
  • Entanglement is a key resource in quantum information processing.
  • Understanding initial condition dependence is crucial for controlling quantum systems.

Purpose of the Study:

  • To analyze the entangling quantum kicked top for few qubits.
  • To investigate the initial condition dependence of time-averaged entanglement (S_Q).
  • To explore the relationship between classical phase space and quantum entanglement.

Main Methods:

  • Analysis of the entangling quantum kicked top model.
  • Focus on few-qubit systems and spin-coherent states.
  • Introduction of a novel measure for classical trajectory behavior.

Main Results:

  • A strong connection exists between classical phase space and initial condition dependence of entanglement (S_Q).
  • This correlation is independent of classical chaos.
  • Entanglement exhibits clear (quasi-)periodicity with the number of kicks and kick strength.

Conclusions:

  • Classical trajectory behavior, not chaos, dictates entanglement dependence on initial conditions.
  • Both classical and quantum initial-condition dependence maps are organized around Hamiltonian symmetry points.
  • The study reveals predictable patterns in quantum entanglement evolution.