Emergence of jumps in quantum trajectories via homogeneization
Abstract
In the strong noise regime, we study the homogeneization of quantum trajectories i.e. stochastic processes appearing in the context of quantum measurement. When the generator of the average semi-group can be separated into three distinct time scales, we start by describing a homogenized limiting semi-group. This result is of independent interest and is formulated outside of the scope of quantum trajectories. Going back to the quantum context, we show that, in the Meyer-Zheng topology, the time-continuous quantum trajectories converge weakly to the discontinuous trajectories of a pure jump Markov process. Notably, this convergence cannot hold in the usual Skorokhod topology.
Keywords
Cite
@article{arxiv.2103.01916,
title = {Emergence of jumps in quantum trajectories via homogeneization},
author = {Tristan Benoist and Cédric Bernardin and Raphaël Chetrite and Reda Chhaibi and Joseph Najnudel and Clément Pellegrini},
journal= {arXiv preprint arXiv:2103.01916},
year = {2023}
}
Comments
48 pages, no figures. v1: Preliminary version. v2: Minor changes in presentation, submitted version