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An Introduction to Quantum Communication

Book Description

Quantum mechanics is the most successful theory for describing the micro-world of photons, atoms, and their aggregates. It is behind much of the successes of the modern technology. It has deep philosophical implications to the fundamental nature of material reality. A few decades ago it was also realized that it is connected to the computer science and information theory. With this understanding was born the new disciplines of quantum computing and quantum communication. The current book introduces the very exciting area of quantum communication which lies at the intersection of quantum mechanics, information theory, and atomic physics. The relevant concepts of these disciplines are explained and their implication for the task of unbreakably secure communication is elucidated. Mathematical formulation of various approaches are explained and attempt has been made to keep the exposition self-contained.

Table of Contents

  1. Cover
  2. Half Title Page
  3. Title Page
  4. Copyright Page
  5. Dedication
  6. Contents
  7. LIST OF FIGURES
  8. 1. WHY QUANTUM COMMUNICATION?
    1. 1.1 Classical Communication and Its Limits
      1. Concept of Probability Distribution
      2. Information or Shannon Entropy
      3. Shannon-Hartley Theorem
      4. Noisy-Channel Coding Theorem
      5. Limits of Classical Communication
    2. 1.2 Role of Quantum Communication
  9. 2. PHYSICAL BASIS OF QUANTUM COMMUNICATION
    1. 2.1 Basic Quantum Mechanics for QC
      1. Wave function
      2. Schrödinger’s Equation
      3. Bra and Ket
      4. Probability Function
      5. Superposition Principle
    2. 2.2 Einstein–Podolsky–Rosen Paradox
    3. 2.3 Some Inequalities
    4. 2.4 Idea of Entanglement
    5. 2.5 Quantum Zeno Effect
    6. 2.6 Decoherence
    7. 2.7 Propagation of Light in an Optical Fiber
  10. 3. INFORMATION THEORY FOR QUANTUM COMMUNICATION
    1. 3.1 Mathematical Representation of a Single Qubit
    2. 3.2 Entropies for Information
      1. Von Neumann Entropy
      2. Shannon Entropy
      3. Renyi Entropy
      4. Collision Entropy
      5. Min-Entropy
      6. Tsallis Entropy
      7. Sharma-Mittal Entropy
    3. 3.3 Shannon-like Capacity Theorems for QC
    4. 3.4 No-Go Theorems for Qubits
    5. 3.5 A General Model for Quantum Communication
    6. 3.6 Entanglement Measures
    7. 3.7 Entanglement Processing
    8. Appendix 3A: Special 3-qubit Quantum States
    9. Appendix 3B: Peres-Horodecky Criterion
    10. Appendix 3C: Von Neumann Entropy
    11. Appendix 3D: Other Information Entropies
  11. 4. QUANTUM ERROR CORRECTION CODING AND CRYPTOGRAPHY
    1. 4.1 Need for Coding in Communication
      1. Source Coding (Classical)
      2. Channel Coding (Classical)
    2. 4.2 Source Coding (Quantum)
    3. 4.3 Error Correction Coding (Quantum): An Example
    4. 4.4 General Error Correction Coding (Quantum)
    5. 4.5 Cryptography: Classical and Quantum
    6. 4.6 A QKD Protocols Based on Heisenberg Uncertainty Principle
    7. 4.7 A QKD Protocol based on Entanglement
    8. 4.8 Practical QKD
  12. 5. QUANTUM COMMUNICATION NETWORK (QCN)
    1. 5.1 A Review of Classical Communication Network
    2. 5.2 Basic QCN Architecture
    3. 5.3 Quantum Teleportation
    4. 5.4 Quantum Super-dense Coding
    5. 5.5 Quantum Repeater Network
    6. 5.6 Software Defined Quantum Networking
  13. 6. PHYSICAL REALIZATION OF QUANTUM COMMUNICATION NETWORK
    1. 6.1 Flying Qubit Sources
    2. 6.2 Stationary Qubit Sources
    3. 6.3 Qubit Detection and Measurement
    4. 6.4 Quantum Repeater (QR)
    5. 6.5 Distributed Quantum Nodes
    6. Appendix 6A: Stationary Qubit Source Technologies
  14. REFERENCE
  15. INDEX