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Quantum decoherence arises due to uncontrollable entanglement between asystem with its environment. However the effects of decoherence are oftenthought of and modeled through a simpler picture in which the role of theenvironment is to introduce classical noise in the system's degrees of freedom.Here we establish necessary conditions that the classical noise models need tosatisfy to quantitatively model the decoherence. Specifically, forpure-dephasing processes we identify well-defined statistical properties forthe noise that are determined by the quantum many-point time correlationfunction of the environmental operators that enter into the system-bathinteraction. In particular, for the exemplifying spin-boson problem with aLorentz-Drude spectral density we show that the high-temperature quantumdecoherence is quantitatively mimicked by colored Gaussian noise. In turn, fordissipative environments we show that classical noise models cannot describedecoherence effects due to spontaneous emission induced by a dissipativeenvironment. These developments provide a rigorous platform to assess thevalidity of classical noise models of decoherence.

When can quantum decoherence be mimicked by classical noise?