# When can quantum decoherence be mimicked by classical noise?

## TL;DR

This paper establishes the conditions under which classical noise models can accurately replicate quantum decoherence, highlighting their limitations and applicability in different environmental scenarios.

## Contribution

It provides necessary criteria for classical noise to model quantum decoherence and demonstrates their validity in specific cases like high-temperature pure-dephasing.

## Key findings

- Classical noise can mimic quantum decoherence in pure-dephasing at high temperatures.
- Classical noise models fail to describe decoherence from spontaneous emission in dissipative environments.
- Necessary conditions relate to the environmental correlation functions and spectral densities.

## Abstract

Quantum decoherence arises due to uncontrollable entanglement between a system with its environment. However the effects of decoherence are often thought of and modeled through a simpler picture in which the role of the environment is to introduce classical noise in the system's degrees of freedom. Here we establish necessary conditions that the classical noise models need to satisfy to quantitatively model the decoherence. Specifically, for pure-dephasing processes we identify well-defined statistical properties for the noise that are determined by the quantum many-point time correlation function of the environmental operators that enter into the system-bath interaction. In particular, for the exemplifying spin-boson problem with a Lorentz-Drude spectral density we show that the high-temperature quantum decoherence is quantitatively mimicked by colored Gaussian noise. In turn, for dissipative environments we show that classical noise models cannot describe decoherence effects due to spontaneous emission induced by a dissipative environment. These developments provide a rigorous platform to assess the validity of classical noise models of decoherence.