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