Linear dynamical quantum systems : analysis, synthesis, and control

• Main Authors: Nurdin, Hendra I. (Author), Yamamoto, Naoki (Author)
• Format: Electronic eBook
• Language: English
• Published: Cham, Switzerland : Springer, 2017.
• Series: Communications and control engineering.
• Subjects: Quantum theory.; Linear systems.; elektronické knihy; electronic books
• ISBN: 9783319552019; 9783319551999
• Physical Description: 1 online resource (xv, 262 pages) : illustrations

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-theo...

Table of 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.