Quantum Information, 2 Volume Set, 2nd Edition

Book description

This comprehensive textbook on the rapidly advancing field introduces readers to the fundamental concepts of information theory and quantum entanglement, taking into account the current state of research and development. It thus covers all current concepts in quantum computing, both theoretical and experimental, before moving on to the latest implementations of quantum computing and communication protocols. It contains problems and exercises and is therefore ideally suited for students and lecturers in physics and informatics, as well as experimental and theoretical physicists in academia and industry who work in the field of quantum information processing.

The second edition incorporates important recent developments such as quantum metrology, quantum correlations beyond entanglement, and advances in quantum computing with solid state devices.

Table of contents

  1. Cover
  2. Preface to the New Edition
  3. Preface to Lectures on Quantum Information (2006)
  4. Volume 1
    1. Part I: Classical Information Theory
      1. 1 Classical Information Theory and Classical Error Correction
        1. 1.1 Introduction
        2. 1.2 Basics of Classical Information Theory
        3. 1.3 Linear Block Codes
        4. 1.4 Further Aspects
        5. References
      2. 2 Computational Complexity
        1. 2.1 Basics
        2. 2.2 Algorithms and Time Complexity
        3. 2.3 Tractable Trails: The Class P
        4. 2.4 Intractable Itineraries: The Class NP
        5. 2.5 Reductions and NP‐Completeness‐Completeness
        6. 2.6 P Versus NP
        7. 2.7 Optimization
        8. 2.8 Complexity Zoo
        9. References
    2. Part II: Foundations of Quantum Information Theory
      1. 3 Discrete Quantum States versus Continuous Variables
        1. 3.1 Introduction
        2. 3.2 Finite‐Dimensional Quantum Systems
        3. 3.3 Continuous‐Variables
        4. References
      2. 4 Approximate Quantum Cloning
        1. 4.1 Introduction
        2. 4.2 The No‐Cloning Theorem
        3. 4.3 State‐Dependent Cloning
        4. 4.4 Phase‐Covariant Cloning
        5. 4.5 Universal Cloning
        6. 4.6 Asymmetric Cloning
        7. 4.7 Probabilistic Cloning
        8. 4.8 Experimental Quantum Cloning
        9. 4.9 Summary and Outlook
        10. References
      3. 5 Channels and Maps
        1. 5.1 Introduction
        2. 5.2 Completely Positive Maps
        3. 5.3 The Choi–Jamiolkowski Isomorphism
        4. 5.4 The Stinespring Dilation Theorem
        5. 5.5 Classical Systems as a Special Case
        6. 5.6 Channels with Memory
        7. 5.7 Examples
        8. References
      4. 6 Quantum Algorithms
        1. 6.1 Introduction
        2. 6.2 Precursors
        3. 6.3 Shor's Factoring Algorithm
        4. 6.4 Grover's Algorithm
        5. 6.5 Other Algorithms
        6. 6.6 Recent Developments
        7. References
      5. 7 Quantum Error Correction
        1. 7.1 Introduction
        2. 7.2 Quantum Channels
        3. 7.3 Using Classical Error‐Correcting Codes
        4. 7.4 Further Aspects
        5. References
    3. Part III: Theory of Entanglement
      1. 8 The Separability versus Entanglement Problem
        1. 8.1 Introduction
        2. 8.2 Bipartite Pure States: Schmidt Decomposition
        3. 8.3 Bipartite Mixed States: Separable and Entangled States
        4. 8.4 Operational Entanglement Criteria
        5. 8.5 Non‐operational Entanglement Criteria
        6. 8.6 Bell Inequalities
        7. 8.7 Quantification of Entanglement
        8. 8.8 Classification of Bipartite States with Respect to Quantum Dense Coding
        9. 8.9 Multipartite States
        10. Acknowledgments
        11. References
      2. 9 Quantum Discord and Nonclassical Correlations Beyond Entanglement
        1. 9.1 Introduction
        2. 9.2 Quantumness Versus Classicality (of Correlations)
        3. 9.3 Quantifying Quantum Correlations – Quantum Discord
        4. 9.4 Interpreting Quantum Correlations – Local Broadcasting
        5. 9.5 Alternative Characterizations of Quantum Correlations
        6. 9.6 General Desiderata for Measures of Quantum Correlations
        7. 9.7 Outlook
        8. References
      3. 10 Entanglement Theory with Continuous Variables
        1. 10.1 Introduction
        2. 10.2 Phase‐Space Description
        3. 10.3 Entanglement of Gaussian States
        4. 10.4 More on Gaussian Entanglement
        5. References
      4. 11 Entanglement Measures
        1. 11.1 Introduction
        2. 11.2 Manipulation of Single Systems
        3. 11.3 Manipulation in the Asymptotic Limit
        4. 11.4 Postulates for Axiomatic Entanglement Measures: Uniqueness and Extremality Theorems
        5. 11.5 Examples of Axiomatic Entanglement Measures
        6. Acknowledgments
        7. References
      5. 12 Purification and Distillation
        1. 12.1 Introduction
        2. 12.2 Pure States
        3. 12.3 Distillability and Bound Entanglement in Bipartite Systems
        4. 12.4 Bipartite Entanglement Distillation Protocols
        5. 12.5 Distillability and Bound Entanglement in Multipartite Systems
        6. 12.6 Entanglement Purification Protocols in Multipartite Systems
        7. 12.7 Distillability with Noisy Apparatus
        8. 12.8 Applications of Entanglement Purification
        9. 12.9 Summary and Conclusions
        10. Acknowledgments
        11. References
      6. 13 Bound Entanglement
        1. 13.1 Introduction
        2. 13.2 Distillation of Quantum Entanglement: Repetition
        3. 13.3 Bound Entanglement – Bipartite Case
        4. 13.4 Bound Entanglement: Multipartite Case
        5. 13.5 Further Reading: Continuous Variables
        6. Exercises
        7. References
      7. 14 Multipartite Entanglement
        1. 14.1 Introduction
        2. 14.2 General Theory
        3. 14.3 Important Classes of Multipartite states
        4. 14.4 Specialized Topics
        5. Acknowledgments
        6. References
    4. Part IV: Quantum Communication
      1. 15 Quantum Teleportation
        1. 15.1 Introduction
        2. 15.2 Quantum Teleportation Protocol
        3. 15.3 Implementations
        4. References
      2. 16 Theory of Quantum Key Distribution (QKD)
        1. 16.1 Introduction
        2. 16.2 Classical Background to QKD
        3. 16.3 Ideal QKD
        4. 16.4 Idealized QKD in Noisy Environment
        5. 16.5 Realistic QKD in Noisy and Lossy Environment
        6. 16.6 Improved Schemes
        7. 16.7 Improvements in Public Discussion
        8. 16.8 Conclusion
        9. References
      3. 17 Quantum Communication Experiments with Discrete Variables
        1. 17.1 Aunt Martha
        2. 17.2 Quantum Cryptography
        3. 17.3 Entanglement‐Based Quantum Communication
        4. 17.4 Conclusion
        5. References
      4. 18 Continuous Variable Quantum Communication with Gaussian States
        1. 18.1 Introduction
        2. 18.2 Continuous‐Variable Quantum Systems
        3. 18.3 Tools for State Manipulation
        4. 18.4 Quantum Communication Protocols
        5. References
  5. Volume 2
    1. Part V: Quantum Computing: Concepts
      1. 19 Requirements for a Quantum Computer
        1. 19.1 Classical World of Bits and Probabilities
        2. 19.2 Logically Impossible Operations?
        3. 19.3 Quantum World of Probability Amplitudes
        4. 19.4 Interference Revisited
        5. 19.5 Tools of the Trade
        6. 19.6 Composite Systems
        7. 19.7 Quantum Circuits
        8. 19.8 Summary
      2. 20 Probabilistic Quantum Computation and Linear Optical Realizations
        1. 20.1 Introduction
        2. 20.2 Gottesman/Chuang Trick
        3. 20.3 Optical Background
        4. 20.4 Knill–Laflamme–Milburn (KLM) Scheme
        5. References
      3. 21 One‐Way Quantum Computation
        1. 21.1 Introduction
        2. 21.2 Simple Examples
        3. 21.3 Beyond Quantum Circuit Simulation
        4. 21.4 Implementations
        5. 21.5 Recent Developments
        6. 21.6 Outlook
        7. Acknowledgments
        8. Exercises
        9. References
      4. 22 Holonomic Quantum Computation
        1. 22.1 Geometric Phase and Holonomy
        2. 22.2 Application to Quantum Computation
        3. References
    2. Part VI: Quantum Computing: Implementations
      1. 23 Quantum Computing with Cold Ions and Atoms: Theory
        1. 23.1 Introduction
        2. 23.2 Trapped Ions
        3. 23.3 Trapped Neutral Atoms
        4. References
      2. 24 Quantum Computing Experiments with Cold Trapped Ions
        1. 24.1 Introduction to Trapped‐Ion Quantum Computing
        2. 24.2 Paul Traps
        3. 24.3 Ion Crystals and Normal Modes
        4. 24.4 Trap Technology
        5. Acknowledgements
        6. References
      3. 25 Quantum Computing with Solid‐State Systems
        1. 25.1 Introduction
        2. 25.2 Concepts
        3. 25.3 Electron Spin Qubits
        4. 25.4 Superconducting Qubits
        5. References
      4. 26 Time‐Multiplexed Networks for Quantum Optics
        1. 26.1 Introduction
        2. 26.2 Multiplexing
        3. 26.3 Photon‐Number‐Resolving Detection with Time Multiplexing
        4. 26.4 Quantum Walks in Time
        5. 26.5 Conclusion
        6. References
      5. 27 A Brief on Quantum Systems Theory and Control Engineering
        1. 27.1 Introduction
        2. 27.2 Systems Theory of Closed Quantum Systems
        3. 27.3 Toward a Systems Theory for Open Quantum Systems
        4. 27.4 Relation to Numerical Optimal Control
        5. 27.5 Outlook on Infinite‐Dimensional Systems
        6. 27.6 Conclusion
        7. Acknowledgments
        8. References
      6. 28 Quantum Computing Implemented via Optimal Control: Application to Spin and Pseudospin Systems
        1. 28.1 Introduction
        2. 28.2 From Controllable Spin Systems to Suitable Molecules
        3. 28.3 Scalability
        4. 28.4 Algorithmic Platform for Quantum Control Systems
        5. 28.5 Applied Quantum Control
        6. 28.6 Worked Example: Unitary Controls for Classifying Knots by NMR
        7. 28.7 Conclusions
        8. Acknowledgments
        9. References
    3. Part VII: Quantum Interfaces and Memories
      1. 29 Cavity Quantum Electrodynamics: Quantum Information Processing with Atoms and Photons
        1. 29.1 Introduction
        2. 29.2 Microwave Cavity Quantum Electrodynamics
        3. 29.3 Optical Cavity Quantum Electrodynamics
        4. 29.4 Conclusions and Outlook
        5. References
      2. 30 Quantum Repeater
        1. 30.1 Introduction
        2. 30.2 Concept of the Quantum Repeater
        3. 30.3 Proposals for Experimental Realization
        4. 30.4 Summary and Conclusions
        5. Acknowledgments
        6. References
      3. 31 Quantum Interface Between Light and Atomic Ensembles
        1. 31.1 Introduction
        2. 31.2 Off‐Resonant Interaction of Light with Atomic Ensemble
        3. 31.3 Entanglement of Two Atomic Clouds
        4. 31.4 Quantum Memory for Light
        5. 31.5 Multiple Passage Protocols
        6. 31.6 Atoms‐Light Teleportation and Entanglement Swapping
        7. 31.7 Quantum Cloning into Atomic Memory
        8. 31.8 Summary
        9. Acknowledgment
        10. References
      4. 32 Echo‐Based Quantum Memory
        1. 32.1 Overview of Photon Echo Techniques
        2. 32.2 Platforms for Echo‐Based Quantum Memory
        3. 32.3 Characterization
        4. 32.4 Demonstrations
        5. 32.5 Outlook
        6. References
      5. 33 Quantum Electrodynamics of a Qubit
        1. 33.1 Quantum Electrodynamics of a Qubit in a Spherical Cavity
        2. 33.2 Suppression of Radiative Decay of a Qubit in a Photonic Crystal
        3. References
      6. 34 Elementary Multiphoton Processes in Multimode Scenarios
        1. 34.1 A Generic Quantum Electrodynamical Model
        2. 34.2 The Multiphoton Path Representation
        3. 34.3 Examples
        4. 34.4 Conclusion
        5. Appendix Evaluation of the Field Commutator
        6. References
    4. Part VIII: Towards Quantum Technology Applications
      1. 35 Quantum Interferometry with Gaussian States
        1. 35.1 Introduction
        2. 35.2 The Interferometer
        3. 35.3 Interferometer with Coherent States of Light
        4. 35.4 Interferometer with Squeezed States of Light
        5. 35.5 Fundamental Limits
        6. 35.6 Summary and Discussion
        7. Problems
        8. References
      2. 36 Quantum Logic‐Enabled Spectroscopy
        1. 36.1 Introduction
        2. 36.2 Trapping and Doppler Cooling of a Two‐Ion Crystal
        3. 36.3 Coherent Atom–Light Interaction and State Manipulation
        4. 36.4 Quantum Logic Spectroscopy for Optical Clocks
        5. 36.5 Photon Recoil Spectroscopy
        6. 36.6 Quantum Logic with Molecular Ions
        7. 36.7 Nonclassical States for Spectroscopy
        8. 36.8 Future Directions
        9. Acknowledgments
        10. References
      3. 37 Quantum Imaging
        1. 37.1 Introduction
        2. 37.2 The Quantum Laser Pointer
        3. 37.3 Manipulation of Spatial Quantum Noise
        4. 37.4 Two‐Photon Imaging
        5. 37.5 Other Topics in Quantum Imaging
        6. 37.6 Conclusion and Perspectives
        7. Acknowledgment
        8. References
      4. 38 Quantum Frequency Combs
        1. 38.1 Introduction
        2. 38.2 Parametric Down Conversion of a Frequency Comb
        3. 38.3 Experiment
        4. 38.4 Experimental Results
        5. 38.5 Application to Quantum Information Processing
        6. 38.6 Application to Quantum Metrology
        7. 38.7 Conclusion
        8. Acknowledgment
        9. References
  6. Index
  7. End User License Agreement

Product information

  • Title: Quantum Information, 2 Volume Set, 2nd Edition
  • Author(s): Dagmar Bruss, Gerd Leuchs
  • Release date: June 2019
  • Publisher(s): Wiley-VCH
  • ISBN: 9783527413539