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Classical noise models can quantitatively mimic quantum decoherence under specific conditions. However, they fail to capture decoherence effects in dissipative environments, highlighting limitations in modeling quantum systems.

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Area of Science:

  • Quantum Physics
  • Quantum Information Science
  • Condensed Matter Physics

Background:

  • Quantum decoherence, a key process in quantum systems, is often modeled using classical noise.
  • The validity of these classical noise models for accurately representing decoherence is frequently assumed rather than rigorously established.
  • Understanding the precise conditions under which classical noise can mimic quantum decoherence is crucial for developing accurate theoretical frameworks and experimental designs.

Purpose of the Study:

  • To establish necessary conditions for classical noise models to quantitatively describe quantum decoherence.
  • To rigorously assess the limitations of classical noise approximations in modeling decoherence phenomena.
  • To identify the specific statistical properties required for classical noise to accurately represent pure-dephasing processes.

Main Methods:

  • Derivation of necessary conditions for classical noise models based on system-environment entanglement.
  • Analysis of quantum many-point time correlation functions of environmental operators.
  • Application to the spin-boson model with a Lorentz-Drude spectral density to exemplify pure-dephasing.
  • Investigation of decoherence in dissipative environments, considering spontaneous emission.

Main Results:

  • Identified well-defined statistical properties for classical noise in pure-dephasing processes, linked to environmental correlation functions.
  • Demonstrated that high-temperature quantum decoherence in the spin-boson model is quantitatively mimicked by colored Gaussian noise.
  • Showed that classical noise models are insufficient to describe decoherence arising from relaxation via spontaneous photon/phonon emission in dissipative environments.

Conclusions:

  • Classical noise models provide a valid quantitative description of decoherence only under specific conditions, particularly for pure-dephasing.
  • The accuracy of classical noise models is fundamentally limited in dissipative systems where relaxation mechanisms are dominant.
  • These findings offer a rigorous framework for evaluating the applicability and limitations of classical noise approximations in the study of quantum decoherence.