product iamge

Quantum Continuous Variables: A Primer of Theoretical Methods

This document was uploaded by one of our users. The uploader already confirmed that they had the permission to publish it. If you are author/publisher or own the copyright of this documents, please report to us by using this DMCA report form.

Download
Search on Amazon

Simply click on the Download Book button.

Yes, Book downloads on Ebookily are 100% Free.

Sometimes the book is free on Amazon As well, so go ahead and hit "Search on Amazon"

Quantum Continuous Variables introduces the theory of continuous variable quantum systems, from its foundations based on the framework of Gaussian states to modern developments, including its applications to quantum information and forthcoming quantum technologies. This book addresses the theory of Gaussian states, operations, and dynamics in great depth and breadth, through a novel approach that embraces both the Hilbert space and phase descriptions.

The second edition of this book has been revised throughout, and updated to include new topics, such as boson sampling, coherent feedback, nonlinear control, as well as several new solved problems.

The volume includes coverage of entanglement theory and quantum information protocols, and their connection with relevant experimental set-ups. General techniques for non-Gaussian manipulations also emerge as the treatment unfolds and are demonstrated with specific case studies.

This book will be of interest to graduate students looking to familiarise themselves with the field, in addition to experienced researchers eager to enhance their understanding of its theoretical methods. It will also appeal to experimentalists searching for a rigorous but accessible treatment of the theory in the area.

Features

    • Provides the first systematic graduate-level textbook for the field of quantum continuous variables and includes 77 problems for the reader, with accompanying solutions

      • Explores applications to entanglement theory, nonlocality, quantum technologies and quantum control

        • Describes, in detail, a comprehensive list of experimental platforms where the formalism applies

        Alessio Serafini earned his PhD from the University of Salerno. He is currently a Professor at University College London. His research focuses mainly on quantum optics, quantum information with continuous variables, and the theory of quantum control.

        Author(s): Alessio Serafini
        Edition: 2
        Publisher: CRC Press/Chapman & Hall
        Year: 2023

        Language: English
        Pages: 361
        City: Boca Raton

        Cover
        Half Title
        Title Page
        Copyright Page
        Contents
        Preface
        Acknowledgments
        Preface to the Second Edition
        List of Problems
        SECTION I: Preliminaries
        Chapter 1: Introduction
        1.1. What is this book about?
        1.1.1. Synopsis
        1.2. How to use this book
        1.3. Mathematical notation, conventions and basic formulae
        1.3.1. Hilbert spaces and operators
        1.3.2. Linear algebra and direct sums
        1.3.2.1. Singular Value Decomposition
        1.3.2.2. Schur Complements
        1.3.3. Compact outer product notation
        1.3.4. Delta functions
        1.3.5. Gaussian integrals
        1.3.6. Miscellanea
        Chapter 2: Quantum Mechanics: Instructions for Use
        2.1. Quantum states and quantum measurements
        2.2. CP-maps and unitary transformations
        2.3. Dynamics: Hamiltonians and master equations
        2.4. Continuous variables
        2.5. Entropies
        2.6. Quantum entanglement
        2.6.1. Entanglement of pure quantum states
        2.6.2. Partial transposition and logarithmic negativity
        2.7. Further reading
        SECTION II: Foundations
        Chapter 3: Gaussian States of Continuous Variable Systems
        3.1. Canonical commutation relations
        3.2. Quadratic Hamiltonians and Gaussian states
        3.2.1. Displacement operators
        3.2.2. The symplectic group of linear canonical transformations
        3.2.3. Normal modes
        3.2.4. Normal mode decomposition of a Gaussian state
        3.2.5. The Fock basis
        3.3. Statistical moments of a Gaussian state and the covariance matrix
        3.4. The uncertainty principle
        3.5. Purity and entropies of Gaussian states
        3.6. Further reading
        Chapter 4: Phase Space Methods
        4.1. Coherent states
        4.2. The Fourier–Weyl relation
        4.3. Characteristic functions and quasi-probability distributions
        4.3.1. General properties of the characteristic function
        4.3.2. Quasi-probability distributions
        4.4. Characteristic function of a Gaussian state
        4.5. Further reading
        SECTION III: Dynamics
        Chapter 5: Gaussian Operations
        5.1. Gaussian unitary transformations
        5.1.1. Linear displacements
        5.1.2. Symplectic transformations
        5.1.2.1. Passive Transformations: Phase Shifters and Beam Splitters
        5.1.2.2. Squeezing Transformations
        5.2. Tensor products and partial traces of Gaussian states
        5.3. Deterministic Gaussian CP-maps
        5.3.1. Dual Gaussian CP-maps and action onWeyl operators
        5.3.2. Classical mixing
        5.3.3. Losses, attenuators and amplifiers
        5.4. Gaussian measurements
        5.4.1. Homodyne detection
        5.4.1.1. Homodyne Generating Function
        5.4.2. Bell measurements and heterodyne detection
        5.4.3. Ideal general-dyne detections
        5.4.4. Noisy measurements
        5.4.5. Conditional Gaussian dynamics
        5.5. Choi–Jamiolkowski description of the most general Gaussian CP-map
        5.5.1. Choi isomorphism and gate teleportation
        5.5.2. Choi isomorphism in infinite dimension
        5.5.3. The most general Gaussian CP-map
        5.6. Further reading
        Chapter 6: Diffusive Dynamics and Continuous Monitoring
        6.1. Linear and quadratic Hamiltonian dynamics
        6.2. Open diffusive dynamics
        6.2.1. Master equations
        6.2.2. Quantum Langevin equations
        6.3. General-dyne filtering of diffusive dynamics
        6.3.1. Stochastic master equations
        6.4. Linear feedback control
        6.5. Optimal filtering of quantum squeezing
        6.6. Diffusive coherent feedback
        6.6.1. Interferometric feedback
        6.6.2. Optimal squeezing through coherent feedback
        6.7. Further reading
        SECTION IV: Correlations
        Chapter 7: Entanglement of Continuous Variable Systems
        7.1. Separability criteria for Gaussian states
        7.1.1. Separability of two-mode Gaussian states
        7.2. A general criterion for Gaussian separability
        7.3. Separability of multi-mode Gaussian states
        7.3.1. 1 vs. n mode Gaussian states
        7.3.2. Locally symmetric states
        7.3.3. Pure and isotropic Gaussian states
        7.4. Logarithmic negativity of Gaussian states
        7.5. Entanglement distillation
        7.5.1. Distilling Gaussian entanglement from non-Gaussian states
        7.6. Higher-order separability criteria
        7.7. Probabilistic entanglement enhancement: Photon subtracted states
        7.8. Quantum nonlocality with continuous variables
        7.9. Further reading
        SECTION V: Technologies
        Chapter 8: Quantum Information Protocols with Continuous Variables
        8.1. Quantum teleportation
        8.1.1. Quantum teleportation of Gaussian states
        8.1.2. Classical threshold for coherent states
        8.2. Classical communication over bosonic channels
        8.2.1. Maximum output entropy of phase-insensitive channels: Gaussian extremality
        8.2.2. Minimum output entropy of phase-insensitive channels
        8.2.3. Classical capacity of phase-insensitive channels
        8.3. Quantum metrology
        8.3.1. Gaussian quantum Fisher information
        8.3.2. Quantum estimation with single-mode Gaussian states
        8.4. Quantum key distribution
        8.4.1. Quantum key distribution with coherent states
        8.5. Boson sampling
        8.5.1. Gaussian boson sampling
        8.6. Further reading
        Chapter 9: A Grand Tour of Continuous Variable Platforms
        9.1. Quantum light
        9.1.1. Classical light
        9.1.2. Canonical quantisation
        9.1.3. Quantum electromagnetic fields in free space
        9.1.4. Input-output interfaces and quantum Langevin equations
        9.1.5. Driven cavities
        9.1.6. Linear optical quantum computing
        9.1.7. Nonlinearities and universal computation with continuous variables
        9.2. Atom-light interactions
        9.2.1. The rotating wave approximation
        9.2.2. Dispersive interactions
        9.3. Quantum optomechanics
        9.3.1. Linearised dynamics
        9.3.2. Sideband driving
        9.4. Trapped ions
        9.4.1. The Cirac–Zoller quantum computer
        9.5. Collective excitations
        9.5.1. Atomic ensembles
        9.5.2. Spin waves and magnons
        9.6. Superconducting degrees of freedom and circuit QED
        9.6.1. Circuit QED
        9.7. Cold bosonic atoms in optical lattices
        9.8. Further reading
        Appendix A: A note on fermions
        Appendix B: Some Notable Facts About the Symplectic Group
        B.1. The orthogonal compact subgroup
        B.2. The singular value decomposition
        Appendix C: The Wiener process
        Appendix D: Selected Mathematical Lore on Quantum Channels
        D.1. The Holevo bound
        D.2. Entanglement breaking channels
        D.3. Phase-contravariant Gaussian channels
        D.3.1. Conjugate channels
        Appendix E: Classical and Quantum Estimation Bounds
        E.1. Classical Fisher information
        E.2. Quantum Fisher information
        References
        Index