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