Quantum Brownian motion as an iterated entanglementbreaking measurement by the environment
Abstract
EinsteinSmoluchowski 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 entanglementbreaking 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 Diósi and Kiefer to the symplectic covariant formalism and compare them with the preferred timescales and Gaussian states associated with the POVM form.
 Publication:

arXiv eprints
 Pub Date:
 July 2015
 arXiv:
 arXiv:1507.04083
 Bibcode:
 2015arXiv150704083J
 Keywords:

 Quantum Physics
 EPrint:
 Updated title, minor typos and typesetting