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Noisy quantum dynamics show a spectral transition between gapless and gapped phases. This transition impacts entanglement entropy scaling and memory loss timescales in quantum systems.

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Area of Science:

  • Quantum Physics
  • Quantum Information Theory
  • Condensed Matter Physics

Background:

  • Noisy quantum dynamics are crucial for understanding real-world quantum systems.
  • Generalized measurements play a key role in quantum information processing.
  • Phase transitions are fundamental concepts in physics, often studied in ground states.

Purpose of the Study:

  • To investigate the spectral properties of noisy quantum dynamics under generalized measurements.
  • To identify and characterize phase transitions in open quantum systems.
  • To explore the relationship between spectral properties and entanglement dynamics.

Main Methods:

  • Utilizing the Lyapunov spectrum derived from singular values of the nonunitary dynamics matrix.
  • Analyzing the entanglement entropy scaling of the dominant Lyapunov vector.
  • Comparing the observed transitions with known ground-state phase transitions.

Main Results:

  • A spectral transition is identified between gapless and gapped phases in noisy quantum dynamics.
  • The gapless phase corresponds to volume-law entanglement, while the gapped phase corresponds to area-law entanglement for the dominant Lyapunov vector.
  • The spectral transition influences the timescales of memory loss and state purification.

Conclusions:

  • A direct correspondence exists between the spectral gap and entanglement entropy scaling in open quantum systems.
  • This spectral transition offers a new perspective on phase transitions in non-equilibrium quantum dynamics.
  • The findings provide insights into the behavior of quantum information in the presence of noise and measurements.