Poisson and Diffusion Approximation of Stochastic Schrodinger equations with Control

TL;DR

This paper rigorously justifies the Poisson and diffusion approximations in quantum measurement control models by deriving them as limits of discrete quantum repeated measurement procedures, with applications to quantum control examples.

Contribution

It provides a mathematical and physical derivation of stochastic Schrödinger equations as limits of discrete models, enhancing understanding of quantum measurement and control.

Findings

Poisson and diffusion approximations are rigorously justified as limits of discrete procedures.

The paper connects continuous stochastic models with discrete quantum measurement processes.

Examples demonstrate the application of control in quantum measurement models.

Abstract

"Quantum trajectories" are solutions of stochastic differential equations of non-usual type. Such equations are called "Belavkin" or "Stochastic Schr\"odinger Equations" and describe random phenomena in continuous measurement theory of Open Quantum System. Many recent investigations deal with the control theory in such model. In this article, stochastic models are mathematically and physically justified as limit of concrete discrete procedures called "Quantum Repeated Measurements". In particular, this gives a rigorous justification of the Poisson and diffusion approximation in quantum measurement theory with control. Furthermore we investigate some examples using control in quantum mechanics.