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Persistent Ballistic Entanglement Spreading with Optimal Control in Quantum Spin Chains.

Ying Lu1, Pei Shi1, Xiao-Han Wang1

  • 1Center for Quantum Physics and Intelligent Sciences, Department of Physics, <a href="https://ror.org/005edt527">Capital Normal University</a>, Beijing 10048, China.

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A magnetic field robustly induces persistent ballistic spreading of entanglement in quantum spin chains, maintaining linear growth of entanglement entropy until maximum values are reached. This control enhances entanglement, even with perturbed initial states.

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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Quantum information science

Background:

  • Entanglement propagation is crucial for understanding quantum many-body dynamics.
  • Entanglement entropy (EE) typically saturates below the maximum, near the Page value, in random unitary evolutions.
  • Ballistic spreading of EE, common in early times, deviates before reaching saturation.

Purpose of the Study:

  • To investigate the effect of magnetic fields on entanglement spreading in quantum spin chains.
  • To explore methods for achieving persistent ballistic spreading of entanglement entropy.
  • To understand how optimal control influences entanglement dynamics and saturation.

Main Methods:

  • Theoretical analysis of quantum spin chains under magnetic fields.
  • Investigating entanglement entropy dynamics and its saturation properties.
  • Perturbing initial states with random pure states (RPSs) to test robustness.

Main Results:

  • A specific magnetic field robustly induces persistent ballistic spreading of entanglement.
  • Linear growth of EE persists until the maximal EE and a flat entanglement spectrum are achieved.
  • Ballistic spreading and enhanced EE are robust even when initial states are perturbed by RPSs.

Conclusions:

  • Optimal magnetic field control can sustain ballistic entanglement spreading to maximal EE.
  • This control strategy enhances entanglement and demonstrates robustness against initial state perturbations.
  • The observed phenomena are attributed to the endomorphism of time evolution under optimal control for RPSs.