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

TL;DR

This paper demonstrates that certain quantum Brownian motion models can be exactly described as a sequence of unitary evolutions interrupted by entanglement-breaking measurements, providing insights into decoherence and pointer states in continuous variable systems.

Contribution

It establishes a formal connection between Markovian quantum Brownian motion and iterated entanglement-breaking measurements, extending previous results to a symplectic covariant framework.

Findings

Identifies a preferred timescale for the dynamics

Shows the dynamics can be decomposed into unitary evolution and measurements

Extends previous results to symplectic covariant formalism

Abstract

Einstein-Smoluchowski diffusion, damped harmonic oscillations, and spatial decoherence are special cases of an elegant class of Markovian quantum Brownian motion models that is invariant under linear symplectic transformations. Here we prove that for each member of this class there is a preferred timescale such that the dynamics, considered stroboscopically, can be rewritten exactly as unitary evolution interrupted periodically by an entanglement-breaking measurement with respect to a fixed overcomplete set of pure Gaussian states. This is relevant to the continuing search for the best way to describe pointer states and pure decoherence in systems with continuous variables, and gives a concrete sense in which the decoherence can be said to arise from a complete measurement of the system by its environment. We also extend some of the results of Di\'{o}si and Kiefer to the symplectic covariant formalism and compare them with the preferred timescales and Gaussian states associated with the POVM form.