# Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics

@inproceedings{Gardiner2004QuantumNA, title={Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics}, author={Crispin W. Gardiner and Paul Zoller}, year={2004} }

From the contents: A Historical Introduction.- Quantum Statistics.- Quantum Langevin Equations.- Phase Space Methods.- Quantum Markov Processes.- Applying the Master Equation.- Amplifiers and Measurement.- Photon Counting.- Interaction of Light with Atoms.- Squeezing.- The Stochastic Schrodinger Equation.- Cascaded Quantum Systems.- Supplement.- Bibliography.- Author Index.- Index.

## 1,184 Citations

Non-Markovian quantum repeated interactions and measurements

- Physics
- 2009

A non-Markovian model of quantum repeated interactions between a small quantum system and an infinite chain of quantum systems is presented. By adapting and applying usual projection operator…

Quantum Stochastic Processes and the Modelling of Quantum Noise

- PhysicsEncyclopedia of Systems and Control
- 2021

An overview of quantum mechanics as a quantum probability theory is given and 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 optic.

Quantum correlation of an optically controlled quantum system

- Physics
- 2012

A precise time-dependent control of a quantum system relies on an accurate account of the quantum interference among the system, the control, and the environment. A diagrammatic technique has been…

Stochastic Processes: From Classical to Quantum

- Physics
- 2019

The goal of this review1 paper is to give an introduction to the mathematics of quantum noise and some of its applications in non-equilibrium statistical mechanics. We start with some reminders from…

Introduction to quantum non-reciprocal interactions: from non-Hermitian Hamiltonians to quantum master equations and quantum feedforward schemes

- Physics
- 2022

These lecture notes from the 2019 Les Houches Summer School on Quantum Information Machines provides a pedagogical introduction to the theory of non-reciprocal quantum interactions and devices. The…

Spectral characterization of non-Gaussian quantum noise: Keldysh approach and application to photon shot noise

- Physics
- 2020

Having accurate tools to describe non-classical, non-Gaussian environmental fluctuations is crucial for designing effective quantum control protocols and understanding the physics of underlying…

Quantum observer for linear quantum stochastic systems

- Physics2012 IEEE 51st IEEE Conference on Decision and Control (CDC)
- 2012

It is shown how a physically realizable quantum observer can be designed, consistent with the laws of quantum mechanics, to obtain coherent quantum observers in linear quantum stochastic systems.

Incoherent quantum algorithm dynamics of an open system with near-term devices

- PhysicsQuantum Inf. Process.
- 2020

This paper investigates a quantum dynamics algorithm for the density matrix obeying the von Neumann equation using an efficient Lagrangian-based approach and considers the dynamics of the ensemble-averaged of disordered quantum systems which is described by Hamiltonian ensemble with a hybrid quantum-classical algorithm.

Collision models in quantum optics

- Physics
- 2017

Abstract Quantum collision models (CMs) provide advantageous case studies for investigating major issues in open quantum systems theory, and especially quantum non-Markovianity. After reviewing their…

Coherent quantum observers for n-level quantum systems

- Physics2013 Australian Control Conference
- 2013

This paper shows how a coherent quantum observer is designed to track the corresponding n-level quantum plant asymptotically in the sense of mean values, and discusses suboptimal quantum observers in thesense of least mean squares estimation.