Stochastic limits of Quantum repeated measurements

TL;DR

This paper studies the long-term behavior of quantum systems under repeated noisy interactions, showing convergence to a stochastic differential equation and highlighting future research directions in quantum algorithms and stochastic analysis.

Contribution

It demonstrates the convergence of quantum systems with noise to a Volterra stochastic differential equation as interactions increase, extending previous work.

Findings

Quantum systems converge to stochastic differential equations

Establishes links between quantum interactions and stochastic calculus

Opens new research avenues in quantum algorithms and stochastic processes

Abstract

We investigate quantum systems perturbed by noise in the form of repeated interactions between the system and the environment. As the number of interactions (aka time steps) tends to infinity, we show, following the works by Pellegrini, that this system converges to the solution of a Volterra stochastic differential equation. This development sets interesting future research paths at the intersection of quantum algorithms, stochastic differential equations, weak convergence and large deviations.