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Einstein-Smoluchowski diffusion, damped harmonic oscillations, and spatialdecoherence are special cases of an elegant class of Markovian quantum Brownianmotion models that is invariant under linear symplectic transformations. Herewe prove that for each member of this class there is a preferred timescale suchthat the dynamics, considered stroboscopically, can be rewritten exactly asunitary evolution interrupted periodically by an entanglement-breakingmeasurement with respect to a fixed overcomplete set of pure Gaussian states.This is relevant to the continuing search for the best way to describe pointerstates and pure decoherence in systems with continuous variables, and gives aconcrete sense in which the decoherence can be said to arise from a completemeasurement of the system by its environment. We also extend some of theresults of Di\'{o}si and Kiefer to the symplectic covariant formalism andcompare them with the preferred timescales and Gaussian states associated withthe POVM form.

Quantum Brownian motion as an iterated entanglement-breaking measurement by the environment