| Description |
1 online resource (xv, 262 pages) : illustrations |
| Series |
Communications and control engineering |
|
Communications and control engineering.
|
| Contents |
Preface; Contents; Notation; 1 Introduction; 1.1 Quantum Feedback Control: A Brief History; 1.2 Classical Linear Systems and Control Theory; 1.2.1 Classical Linear Systems; 1.2.2 Linear Systems and Control Theory; 1.2.3 Toward Systems and Control Theory for Linear Quantum Systems; 1.3 Closed Linear Quantum Systems; 1.4 Open Quantum Systems, the Markov #x83;; 1.4.1 Open Quantum Systems; 1.4.2 Illustration of the Markov Approximation and Markov Open Quantum System Dynamics; 1.5 Linear Dynamical Quantum Systems: Description and Physical Examples; 1.5.1 Optical Cavities |
|
1.5.2 Non-degenerate Optical Parametric Amplifiers1.5.3 Degenerate Parametric Amplifiers/Optical Parametric Oscillators; 1.5.4 Opto-mechanical Systems; 1.5.5 Large Atomic Ensemble; References; 2 Mathematical Modeling of Linear Dynamical Quantum Systems; 2.1 Quantum Stochastic Calculus; 2.1.1 The Boson Fock Space, Exponential Vectors, and Fundamental Processes on the Fock Space; 2.1.2 Adapted Processes and Quantum Stochastic Integrals; 2.1.3 The Quantum Itō Table in Vacuum and the Quantum Itō Rule; 2.1.4 The Hudson -- Parthasarathy Quantum Stochastic Differential Equation |
|
2.2 Linear Dynamical Quantum Systems: Joint Unitary Evolution of Oscillators and Boson Fields2.3 Equations of Motion: Real Quadrature Form and Complex Mode Form; 2.3.1 Real Quadrature Form; 2.3.2 Complex Mode Form; 2.3.3 Transfer Function of Linear Dynamical Quantum Systems; 2.4 Inclusion of Idealized Static Transformations on Bosonic Fields #x83;; 2.4.1 Completely Passive Linear Dynamical Quantum Systems; 2.5 Physical Realizability Conditions and Parameterizations #x83;; 2.5.1 Physical Realizability Conditions for Linear QSDEs; 2.5.2 Parameterization of Linear Dynamical Quantum Systems |
|
2.5.3 Linear Dynamical Quantum Systems with Less Outputs Than Inputs2.6 Stability of Linear Quantum Systems; 2.7 Gaussian States; 2.7.1 Gaussian State of a Collection of Single-Mode Oscillators; 2.7.2 Gaussian States of the Field and Their Fock Space Representation; 2.7.3 Coherent States; 2.7.4 Coherent States of a Single-Mode Oscillator; 2.7.5 Coherent States of a Bosonic Field; References; 3 Realization Theory for Linear Dynamical Quantum Systems; 3.1 Architecture for Strict Realization; 3.1.1 The Concatenation and Series Product and Reducible Quantum Networks; 3.1.2 Main Synthesis Theorem |
|
3.1.3 Systematic Synthesis of Linear Quantum Systems3.1.4 Illustrative Synthesis Example; 3.2 Architecture for Strict Realization Using Quantum Feedback Networks; 3.2.1 The Model Matrix and Concatenation of Model Matrices; 3.2.2 Edges, Elimination of Edges, and Reduced Markov Models; 3.2.3 Main Synthesis Results; 3.2.4 Synthesis of Completely Passive Systems; 3.3 Transfer Function Realization; 3.3.1 Pure Cascade Realization of the Transfer Function of Linear Quantum Systems; 3.3.2 Conditions for Realizability by a Pure Cascade Connection |
| Summary |
This monograph provides an in-depth treatment of the class of linear-dynamical quantum systems. The monograph presents a detailed account of the mathematical modeling of these systems using linear algebra and quantum stochastic calculus as the main tools for a treatment that emphasizes a system-theoretic point of view and the control-theoretic formulations of quantum versions of familiar problems from the classical (non-quantum) setting, including estimation and filtering, realization theory, and feedback control. Both measurement-based feedback control (i.e., feedback control by a classical system involving a continuous-time measurement process) and coherent feedback control (i.e., feedback control by another quantum system without the intervention of any measurements in the feedback loop) are treated. Researchers and graduates studying systems and control theory, quantum probability and stochastics or stochastic control whether from backgrounds in mechanical or electrical engineering or applied mathematics will find this book to be a valuable treatment of the control of an important class of quantum systems. The material presented here will also interest physicists working in optics, quantum optics, quantum information theory and other quantum-physical disciplines |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed May 22, 2017) |
| Subject |
Quantum theory.
|
|
Linear systems.
|
|
Quantum physics (quantum mechanics & quantum field theory)
|
|
Cybernetics & systems theory.
|
|
Optical physics.
|
|
Automatic control engineering.
|
|
SCIENCE -- Energy.
|
|
SCIENCE -- Mechanics -- General.
|
|
SCIENCE -- Physics -- General.
|
|
Linear systems
|
|
Quantum theory
|
| Form |
Electronic book
|
| Author |
Yamamoto, Naoki, author
|
| ISBN |
9783319552019 |
|
3319552015 |
|
