Emergence of jumps in quantum trajectories via homogeneization

TL;DR

This paper investigates how quantum trajectories behave under strong noise, demonstrating that they converge to jump processes in a specific topology, revealing new insights into quantum measurement dynamics.

Contribution

It introduces a homogenization approach for quantum trajectories with multiple time scales and proves convergence to jump processes in Meyer-Zheng topology, extending understanding beyond traditional frameworks.

Findings

Quantum trajectories converge to jump processes under strong noise.

Homogenization yields a limiting semi-group outside quantum context.

Weak convergence occurs in Meyer-Zheng topology, not Skorokhod.

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.