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Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition.

Soonwon Choi1, Yimu Bao1, Xiao-Liang Qi2

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We discovered two stable phases in open quantum systems, where information scrambling protects quantum information. A phase transition occurs when error rates exceed a threshold, impacting entanglement entropy dynamics.

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Area of Science:

  • Quantum Information Science
  • Condensed Matter Physics
  • Quantum Error Correction

Background:

  • Entanglement entropy dynamics in open quantum systems are complex.
  • Understanding these dynamics is crucial for quantum computing and information processing.
  • Existing models often lack independent control over information scrambling and error rates.

Purpose of the Study:

  • To analyze entanglement entropy dynamics in a generic quantum many-body open system.
  • To introduce and study a novel random unitary circuit model with controllable parameters.
  • To understand the role of information scrambling and projective measurements in phase transitions.

Main Methods:

  • Developed a random unitary circuit model with intermittent projective measurements.
  • Independently controlled information scrambling (unitary evolution) and error rates (projective measurements).
  • Utilized numerical simulations to confirm theoretical predictions and map the phase diagram.

Main Results:

  • Identified two stable phases characterized by volume-law and area-law scaling of entanglement entropy.
  • Demonstrated that chaotic unitary evolution acts as a quantum error correction mechanism.
  • Found a phase transition when error rates surpass a threshold dependent on information scrambling.

Conclusions:

  • Information scrambling is critical for understanding entanglement dynamics in open quantum systems.
  • The entanglement phase transition is linked to changes in quantum channel capacity.
  • The model provides a framework for studying quantum information protection and error correction in realistic quantum systems.