Asymptotic Equivalence of Quantum Stochastic Models

TL;DR

This paper develops a framework for understanding the asymptotic behavior of quantum stochastic models under perturbations, enabling the replacement of complex models with simpler equivalent ones in various quantum physical scenarios.

Contribution

It introduces the concept of asymptotic equivalence of quantum stochastic models via series product perturbations, allowing for model simplification in large parameter regimes.

Findings

Models can be replaced by asymptotically equivalent simpler models.

Examples include virtual work principle, noise commutativity, and polarization channel decoupling.

Application to quantum local asymptotic normality.

Abstract

We introduce the notion of perturbations of quantum stochastic models using the series product, and establish the asymptotic convergence of sequences of quantum stochastic models under the assumption that they are related via a right series product perturbation. While the perturbing models converge to the trivial model, we allow that the individual sequences may be divergent corresponding to large model parameter regimes that frequently occur in physical applications. This allows us to introduce the concept of asymptotically equivalent models, and we provide several examples where we replace one sequence of models with an equivalent one tailored to capture specific features. These examples include: a series product formulation of the principle of virtual work; essential commutativity of the noise in strong squeezing models; the decoupling of polarization channels in scattering by Faraday rotation driven by a strong laser field; and an application to quantum local asymptotic normality.