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Decoherence impacts quantum critical states, altering entanglement. This study reveals universal scaling laws for entanglement and introduces renormalization group flow between quantum channels, with implications for quantum simulators.

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Area of Science:

  • Quantum Information Theory
  • Condensed Matter Physics
  • Quantum Many-Body Systems

Background:

  • Quantum critical states are highly sensitive to environmental interactions.
  • Decoherence, often modeled by quantum channels, degrades quantum information and entanglement.
  • Understanding decoherence effects is crucial for quantum computing and simulation.

Purpose of the Study:

  • To analyze the impact of decoherence on quantum critical states.
  • To investigate universal properties of entanglement in decohered mixed states.
  • To establish a framework for renormalization group (RG) flow between quantum channels.

Main Methods:

  • Modeling decoherence using local quantum channels.
  • Analyzing Renyi entropies and entanglement negativity in decohered states.
  • Utilizing conformal field theory (CFT) and boundary condition changing operators.
  • Numerical verification using the transverse-field Ising model.

Main Results:

  • Renyi entropies show volume law scaling with a CFT 'g function' constant, defining RG flow.
  • Subsystem entropy exhibits subleading logarithmic scaling related to CFT operators.
  • Entanglement negativity displays log or area law scaling depending on RG flow, with continuous changes possible.
  • Identified four RG fixed points for dephasing channels in the Ising model.

Conclusions:

  • Decoherence introduces universal scaling properties to entanglement in quantum critical states.
  • The study provides a method to define and analyze RG flow between quantum channels.
  • Results are applicable to noisy quantum simulators and can be probed using shadow tomography.