Linear Dynamical Quantum Systems Analysis, Synthesis, and Control

This monograph provides an in-depth treatment of the class of linear-dynamical quantum systems. It presents a detailed account of the mathematical modelling of these systems using linear algebra and quantum stochastic calculus as the main tools for a treatment that emphasises a system-theoretic poin...

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Main Author Nurdin, Hendra I
Format eBook Book
LanguageEnglish
Published Cham Springer Nature 2017
Springer
Springer International Publishing AG
Springer International Publishing
Edition1
SeriesCommunications and Control Engineering
Subjects
Control and Systems Theory
Engineering
Nonlinear systems
Other branches of engineering
Quantum Information Technology, Spintronics
Quantum Optics
Quantum Physics
Quantum systems
Systems theory
Systems Theory, Control
Online AccessGet full text
ISBN9783319552019
3319552015
331955199X
9783319551999
ISSN0178-5354
2197-7119
DOI10.1007/978-3-319-55201-9

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Abstract This monograph provides an in-depth treatment of the class of linear-dynamical quantum systems. It presents a detailed account of the mathematical modelling of these systems using linear algebra and quantum stochastic calculus as the main tools for a treatment that emphasises 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, realisation theory and feedback control.
AbstractList This monograph provides an in-depth treatment of the class of linear-dynamical quantum systems. It presents a detailed account of the mathematical modelling of these systems using linear algebra and quantum stochastic calculus as the main tools for a treatment that emphasises 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, realisation theory and feedback control.
Author Yamamoto, Naoki
Nurdin, Hendra I
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Notes Includes bibliographical references and index
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Snippet This monograph provides an in-depth treatment of the class of linear-dynamical quantum systems. It presents a detailed account of the mathematical modelling of...
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SubjectTerms Control and Systems Theory
Engineering
Nonlinear systems
Other branches of engineering
Quantum Information Technology, Spintronics
Quantum Optics
Quantum Physics
Quantum systems
Systems theory
Systems Theory, Control
Subtitle Analysis, Synthesis, and Control
TableOfContents Intro -- 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 ƒ -- 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 Amplifiers -- 1.5.3 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 Fields -- 2.3 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 ƒ -- 2.4.1 Completely Passive Linear Dynamical Quantum Systems -- 2.5 Physical Realizability Conditions and Parameterizations ƒ -- 2.5.1 Physical Realizability Conditions for Linear QSDEs -- 2.5.2 Parameterization of Linear Dynamical Quantum Systems
4.4 Robust Linear Quantum Observers -- 4.4.1 Guaranteed-Error Robust Observer -- 4.4.2 Example -- 4.4.3 Further Reading -- References -- 5 Feedback Control of Linear Dynamical Quantum Systems -- 5.1 Measurement-Based Quantum Feedback Control -- 5.1.1 Controlled Quantum Evolution and Quantum Filter -- 5.1.2 Measurement-Based LQG Control -- 5.2 Coherent Feedback Quantum LQG Control -- 5.2.1 Reformulating the Quantum LQG Problem into a Rank-Constrained LMI Problem -- 5.2.2 Numerically Solving the Rank-Constrained LMI Problem -- 5.2.3 An Extension of the Numerical Procedure -- 5.2.4 Quantum LQG Control Design Examples -- 5.2.5 Quantum LQG Controller Design Example II -- 5.2.6 Further Reading -- 5.3 Coherent Feedback Hinfty Control -- 5.3.1 Dissipation Properties -- 5.3.2 Hinfty Controller Synthesis -- 5.3.3 Hinfty Synthesis in Quantum Optics -- 5.4 Further Reading -- References -- 6 Linear Systems and Control Theory for Quantum Information -- 6.1 Dissipative Generation of Pure Gaussian States -- 6.1.1 General Condition for Pure Gaussian State Generation -- 6.1.2 Synthesizing a Dissipative Gaussian System -- 6.1.3 Gaussian Cluster State Generation via Dissipation -- 6.1.4 A QSDE Formalism -- 6.1.5 Remarks and Further Reading -- 6.2 Enhancing Continuous-Variable EPR Entanglement -- 6.2.1 Stability Condition -- 6.2.2 The Ideal Lossless Case -- 6.2.3 Effect of Losses -- 6.2.4 Comparison with Conventional Schemes -- 6.2.5 Effect of Nonzero Transmission Delays -- 6.3 Force Sensing and Back-Action Evasion -- 6.3.1 Back-Action Evasion and the Standard Quantum Limit -- 6.3.2 System Theoretical Characterization of BAE -- 6.3.3 Coherent Feedback for BAE -- 6.3.4 Further Reading -- 6.4 Quantum Memory with Decoherence-Free Subsystem -- 6.4.1 General Schematic of an Ideal Quantum Memory -- 6.4.2 The Zero Dynamics Principle -- 6.4.3 Perfect State Transfer
2.5.3 Linear Dynamical Quantum Systems with Less Outputs Than Inputs -- 2.6 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 Systems -- 3.1.4 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 -- 3.3.3 Transfer Function Realization of Completely Passive Linear Quantum Systems -- 3.3.4 Further Reading -- References -- 4 Quantum Filtering for Linear Dynamical Quantum Systems -- 4.1 Quantum Conditional Expectations -- 4.1.1 Quantum Probability Space -- 4.1.2 Conditional Expectations -- 4.2 Quantum Filtering Theory -- 4.2.1 Quantum Filtering: The Idea -- 4.2.2 Quantum Filter: Multiple-Input Multiple-Output Case -- 4.2.3 Stochastic Master Equation -- 4.2.4 QND Interaction and the Projection Postulate -- 4.3 Quantum Kalman Filter for Gaussian Linear Quantum Systems -- 4.3.1 Example in Quantum Optics -- 4.3.2 Quantum Filtering: Multiple-Input and Multiple-Output Case
6.4.4 Further Reading -- 6.5 Robust Quantum Amplification via Coherent Feedback -- 6.5.1 The Phase-Preserving Amplifier -- 6.5.2 Coherent Feedback Control for a Quantum Amplifier -- 6.5.3 Example: Non-degenerate Optical Parametric Amplifier -- 6.5.4 Added Noise -- 6.6 Feedback Control Experiments -- 6.6.1 Coherent Feedback for Optical Squeezing Enhancement -- 6.6.2 Measurement-Based Feedback for Spin Squeezing in Atomic Ensemble -- 6.6.3 Further Reading -- References -- Index
Title Linear Dynamical Quantum Systems
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