# Quantum Stochastic Processes and the Modelling of Quantum Noise

## TL;DR

This paper reviews quantum probability theory and introduces quantum stochastic processes, illustrating their connection to quantum Markov models and the quantum regression theorem, providing a foundational overview of quantum noise modeling.

## Contribution

It formulates quantum stochastic processes within quantum probability theory and connects them to quantum Markov models and the quantum regression theorem.

## Key findings

- Quantum stochastic processes are formulated as a generalization of classical stochastic processes.
- Quantum Markov models from quantum optics illustrate the abstract concepts.
- The connection between quantum stochastic processes and the quantum regression theorem is established.

## Abstract

This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum stochastic processes is formulated as a generalization of stochastic processes within the framework of quantum probability theory. Quantum Markov models from quantum optics are used to explicitly illustrate the underlying abstract concepts and their connections to the quantum regression theorem from quantum optics.