Advanced Quantum Communications An Engineering Approach

Advanced Quantum Communications An Engineering Approach

Advanced Quantum Communications: An Engineering Approach by Sandor Imreand Laszlo Gyongyosi

Contents of Advanced Quantum Communications eBook

  • CHAPTER 1. INTRODUCTION 
  • Emerging Quantum Influences
  • Quantum Information Theory
  • Different Capacities of Quantum Channels
  • Challenges Related to Quantum Channel Capacities
  • Secret and Private Quantum Communication
  • Quantum Communications Networks
  • Recent Developments and Future Directions
  • CHAPTER 2. INTRODUCTION TO QUANTUM INFORMATION THEORY 
  • Introduction
  • Brief History
  • Basic Definitions and Formulas
  • Density Matrices and Trace Operator
  • Quantum Measurement
  • Orthonormal Basis Decomposition
  • The Projective and POVM Measurement
  • Partial Trace
  • The Postulates of Quantum Mechanics Using Density Matrices
  • Geometrical Interpretation of the Density Matrices
  • Density Matrices in the Bloch Sphere
  • The Quantum Channel
  • Quantum Entanglement
  • Entropy of Quantum States
  • The von Neumann Entropy of a Density Matrix of Orthogonal States
  • Important Properties of the von Neumann Entropy
  • Classical Entropies
  • Quantum Conditional Entropy
  • Quantum Mutual Information
  • Classical Relative Entropy
  • Quantum Relative Entropy
  • Quantum Rényi-Entropy
  • Measurement of the Amount of Entanglement
  • Entanglement of Formation
  • Entanglement Distillation
  • Encoding Classical Information to Quantum States
  • Encoding to Orthogonal States
  • Encoding to Pure Non-Orthogonal or Mixed States
  • Examples of Orthogonal and Non-Orthogonal Pure State Coding
  • The von Neumann Entropy of a Density Matrix of
  • Non-Orthogonal States
  • Quantum Noiseless Channel Coding
  • Compression with the Non-Orthogonal Encoder
  • Brief Summary
  • Further Reading
  • CHAPTER 3. THE CLASSICAL CAPACITIES OF QUANTUM CHANNELS 
  • Introduction
  • Preliminaries
  • Interaction with the Environment
  • Quantum Channel Capacity
  • Formal Model of a Quantum Channel
  • From Classical to Quantum Communication Channels
  • Transmission of Classical Information over Quantum Channels
  • Various Classical Capacities of Quantum Channels
  • Encoding/Decoding Settings for Unentangled Classical Capacity of
  • Quantum Channels
  • Chain Structure of Quantum Channels
  • Characterization of Encoder and Decoder Settings
  • The Holevo-Schumacher-Westmoreland Theorem
  • Examples: HSW Capacity of Ideal and Zero-Capacity Quantum Channels
  • Classical Communication over Quantum Channels
  • The Classical Capacity of a Quantum Channel
  • From the Holevo Quantity to the HSW Capacity
  • The Private Capacity
  • The Entanglement-Assisted Classical Capacity
  • Brief Summary of Classical Capacities
  • Multilevel Quantum Systems and Qudit Channels
  • Capacity of Qudit Channels
  • The Zero-Error Capacity of a Quantum Channel
  • Characterization of Quantum and Classical Zero-Error Capacities of
  • Quantum Channels
  • Distinguishability of Quantum States with Zero-Error
  • Formal Definitions of Quantum Zero-Error Communication
  • Achievable Zero-Error Rates in Quantum Systems
  • Connection with Graph Theory
  • Entanglement-Assisted Classical Zero-Error Capacity
  • Example of Entanglement-Assisted Zero-Error Capacity
  • Brief Summary
  • Other Code Constructions for Entanglement-Assisted Classical
  • Zero-Error Capacity
  • Further Reading
  • CHAPTER 4. THE QUANTUM CAPACITY OF QUANTUM CHANNELS 
  • Introduction
  • Transmission of Quantum Information
  • Encoding of Quantum Information
  • Transmission of Quantum Information in Codewords
  • Quantum Fidelity of Transmission of Quantum Information
  • Maximizing Quantum Fidelity
  • Quantum Coherent Information
  • Connection between Classical and Quantum Information
  • Quantum Capacity of the Classical Ideal Quantum Channel
  • Quantum Coherent Information versus Quantum Mutual Information
  • Quantum Coherent Information of an Ideal Channel
  • The Asymptotic Quantum Capacity
  • The Lloyd-Shor-Devetak Channel Capacity
  • The Assisted Quantum Capacity
  • Relation between Classical and Quantum Capacities of Quantum Channels
  • Further Reading
  • CHAPTER 5. GEOMETRIC INTERPRETATION OF QUANTUM CHANNELS 
  • Introduction
  • Geometric Interpretation of the Quantum Channels
  • The Tetrahedron Representation
  • Quantum Channel Maps in Tetrahedron Representation
  • Description of Channel Maps  
  • Non-Unital Quantum Channel Maps
  • Geometric Interpretation of the Quantum Informational Distance
  • Quantum Informational Ball
  • Geometric Interpretation of HSW Channel Capacity
  • Quantum Relative Entropy in the Bloch Sphere Representation
  • Derivation of Quantum Relative Entropy on the Bloch
  • Sphere
  • The HSW Channel Capacity and the Radius
  • Quantum Delaunay Triangulation
  • Preliminaries
  • Delaunay Triangulation in the Quantum Space
  • Computation of Smallest Quantum Ball to Derive the HSW Capacity
  • Step : Construction of Delaunay Triangulation
  • Step : The Core-Set Algorithm
  • The Basic Algorithm
  • The Improved Algorithm
  • Illustrative Example
  • Geometry of Basic Quantum Channel Models
  • The Flipping Channel Models
  • The Depolarizing Channel Model
  • The Effect of Decoherence
  • The Amplitude Damping Channel Model
  • The Dephasing Channel Model
  • The Pancake Map
  • Geometric Interpretation of HSW Capacities of Different Quantum Channel Models
  • Illustration of Determination of HSW Channel Capacity
  • Geometric Approach to Determining the Capacity of Unital Quantum
  • Channel Models
  • Analytical Derivation of the HSW Channel Capacity of Depolarizing
  • Quantum Channel
  • A Geometric Way to Determine the Capacity of Depolarizing Quantum Channels
  • A Geometric Way to Determine the Capacity of Amplitude Damping
  • Quantum Channel
  • Further Reading
  • CHAPTER 6. ADDITIVITY OF QUANTUM CHANNEL CAPACITIES 
  • Introduction
  • Introduction to the Additivity Problem of Quantum Channels
  • The Four Propositions for Additivity
  • Additivity of Classical Capacity
  • Additivity of Quantum Capacity
  • The Degradable Quantum Channel
  • Description of Degrading Maps
  • On the Additivity for Degradable and Non-degradable Quantum
  • Channels
  • The Hadamard and Entanglement-Breaking Channels
  • The Noiseless Ideal Quantum Channel
  • Additivity of Holevo Information
  • Computing the Holevo Information
  • Product State Inputs
  • Entangled Inputs
  • Maximization of Joint Holevo Information
  • Maximization for Idealistic Quantum Channels
  • Maximization for General Noisy Channels
  • Conclusions
  • Geometric Interpretation of Additivity of HSW Capacity
  • Geometric Representation of Channel Additivity
  • Quantum Superball and Minimal Entropy States
  • Factoring the Quantum Relative Entropy Function
  • Brief Summary of the Superball Approach
  • Example with Unital Channels
  • Additivity Analysis of Depolarizing Channels
  • Additivity Analysis of Amplitude Damping Quantum
  • Channels
  • Conclusions on Additivity Analysis
  • Classical and Quantum Capacities of some Channels
  • The Classical Zero-Error Capacities of some Quantum Channels
  • Zero-Error Capacity of Bit Flip Channel
  • Zero-Error Capacity of Depolarizing Channel
  • Further Reading
  • CHAPTER 7. SUPERACTIVATION OF QUANTUM CHANNELS 
  • Introduction
  • The Non-Additivity of Private Information
  • Erasure Quantum Channel
  • Channel Combination for Superadditivity of Private Information
  • The First Channel
  • Retro-Correctable Quantum Channel
  • Random Phase Coupling Channel
  • Superactivation of Quantum Capacity of Zero-Capacity Quantum
  • Channels
  • Superactivation with the Horodecki Channel
  • The Four-Dimensional Horodecki Channel
  • Illustrative Example for Superactivation with the Horodecki Channel
  • The Key, the Flag, and the Twister
  • Quantum Capacity of the Joint Structure
  • Superactivation with Four-Dimensional Horodecki and Erasure Channels
  • Small Single-Use and Large Asymptotic Superactivated Quantum Capacity
  • Behind Superactivation: The Information Theoretic Description
  • System Model
  • Output System Description
  • Geometrical Interpretation of Quantum Capacity
  • Example of Geometric Interpretation of Superactivation
  • Extension of Superactivation for More General Classes
  • Properties of the Joint Channel Construction
  • The More Noise, the More Quantum Capacity
  • Conclusions
  • Superactivation of Zero-Error Capacities
  • Superactivation in the Future’s Quantum Communications Networks
  • Theoretical Results on the Superactivation of Zero-Error Capacity
  • Channel Setting for Superactivation
  • Geometric Superactivation of Zero-Error Capacities of a Quantum
  • Channel
  • Classical Zero-Error Capacity
  • Quantum Zero-Error Capacity
  • Further Reading
  • CHAPTER 8. QUANTUM SECURITY AND PRIVACY 
  • Introduction
  • Quantum Key Distribution
  • QKD Implementations
  • Physical Properties of Optical and Free-Space Quantum Channels
  • Attacks against QKD
  • Private Communication over the Quantum Channel
  • Quantum Cryptographic Primitives
  • Quantum Bit Commitment
  • Quantum Bit Commitment without Entanglement: The Hiding Property
  • Entanglement-Assisted Quantum Bit Commitment: The Binding Property
  • Quantum Fingerprinting
  • Description of Quantum Fingerprinting
  • The Quantum Public Key Cryptography
  • Description of Quantum Public Key Scheme
  • Eve’s Attack on the Quantum Public Key Method
  • Security of the Quantum Public Key Protocol
  • Multi-Bit Quantum Public Key Protocol
  • Further Reading
  • CHAPTER 9. QUANTUM COMMUNICATION NETWORKS 
  • Long-Distance Quantum Communications
  • General Model of Quantum Repeater
  • Brief Summary
  • Levels of Entanglement Swapping
  • Scheduling Techniques of Purification
  • Symmetric Scheduling Algorithm
  • Pumping Scheduling Algorithm
  • Greedy Scheduling Algorithm
  • Banded Scheduling Algorithm
  • Hybrid Quantum Repeater
  • Experimental Demonstration of Entanglement Sharing
  • Performance Analysis of Hybrid Quantum Repeater
  • Experimental Results
  • Probabilistic Quantum Networks
  • Conclusions
  • Further Reading
  • CHAPTER 10. RECENT DEVELOPMENTS AND FUTURE DIRECTIONS 
  • Introduction
  • Qubit Implementations
  • Optically Controlled Quantum Bits in Future Quantum Computers
  • The Non-Demolition Sum Gate
  • Microwave and Polarized Laser Controlled Quantum Computers
  • A Silicon Quantum Dot
  • Single-Photon Quantum Bit
  • Solid State–Photon Entanglement
  • Quantum CPUs
  • Controlling the Quantum States of a Quantum Computer
  • Trapped Ion Quantum Chip
  • Trapped Electron Quantum Chip
  • Electrical Control of the Quantum States
  • Optical Random Walk Quantum Chip
  • Quantum Memories
  • Various Experimental Approaches
  • Atomic Frequency Comb with Crystals
  • Centers in Diamond
  • Quantum Dot
  • Single Atoms in Free Space
  • Room-Temperature Gas
  • Ultra-Cold Gas
  • Raman Gas
  • Comparison of Quantum Memories
  • Quantum Memory Implementations
  • Reading a Qubit Two Times
  • Silicon-Bismuth in Quantum Memories
  • Quantum Hard Disk
  • Conversion of Light to Atomic Spin
  • Reducing the Decoherence in Quantum Memories
  • Pyramid Structure
  • Transversal Encoded Quantum Gate Sets
  • Scheme for High Loss Tolerance

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