Quantum Communication.The Physical Layer of Future Optical Networks

Contents
About the Author
Preface
1. Introduction and Basic Concepts
	1.1. Introduction
		1.1.1. Why Quantum Networks?
		1.1.2. Light as a Precious Resource for Communication
		1.1.3. Basic Concepts in Quantum Communication
	1.2. Introduction to Quantum Mechanics
		1.2.1. Postulates of Quantum Mechanics
		1.2.2. Hamiltonian and Schrödinger Equation
		1.2.3. Constant Potential
		1.2.4. Harmonic Oscillator
		1.2.5. Quantization of a Harmonic Oscillator’s Energy
		1.2.6. Energies of a 1D Harmonic Oscillator
		1.2.7. Example: Normalization
		1.2.8. Example: Time Evolution
		1.2.9. Example: Uncertainty in Energy of a Harmonic Oscillator
		1.2.10. Tunneling
	1.3. Dirac Notation
		1.3.1. Wavefunction Properties in Dirac Notation
		1.3.2. Vectorial Representation of Wave Functions
		1.3.3. Basis Functions
		1.3.4. Operators in Dirac Notation
		1.3.5. Example: Projective Measurement
	1.4. Density Operator
		1.4.1. Example: Density Matrix of a Qubit
	1.5. Commutation Relation
		1.5.1. Quantum Microscope
		1.5.2. Calculation of Uncertainty
		1.5.3. Fourier Transform and Uncertainty Relation
	1.6. Entanglement
		1.6.1. The Schrödinger’s Cat
		1.6.2. Quantum Entanglement and Correlation
		1.6.3. Measurement of Quantum Entanglement and Correlation
		1.6.4. Bell Inequality
		1.6.5. Generation of Quantum Optical Entanglement
		1.6.6. Generation of Matter–Matter Entanglement
2. Photons and Atoms for Quantum Optical Information
	2.1. Quantum Electromagnetic Fields
		2.1.1. Classical EM Theory — Maxwell’s Equations
		2.1.2. Classical EM Theory — Solution to Maxwell’s Equations
		2.1.3. Quantum EM Theory
		2.1.4. Quantized EM Fields
		2.1.5. Field Quantization
		2.1.6. Quantized Field Operators
		2.1.7. Coherent States of Light
		2.1.8. Energy–Time Uncertainty
		2.1.9. Homodyne Measurement
		2.1.10. Coherent State in Number Basis
		2.1.11. Beam Splitter in Quantum Optics
		2.1.12. Probability Distribution of Photons in Coherent States
		2.1.13. Quantum Optical Encoding
		2.1.14. Quasi-Probability Distribution
	2.2. Optical Resonators
		2.2.1. Fabry–Perot Optical Resonators
		2.2.2. Examples of Optical Resonators
		2.2.3. Application of EM Resonators in Quantum Technology
	2.3. Photon Correlation
		2.3.1. Second-Order Correlation Function
		2.3.2. Hong–Ou–Mandel Interference
	2.4. Atoms
		2.4.1. Quantization of Energy in Atoms
		2.4.2. Two-Level Atom and Bloch Sphere
		2.4.3. Atomic Operators
	2.5. Light–Atom Interactions
		2.5.1. Absorption and Emission
		2.5.2. Atomic Dipole
		2.5.3. Light–Atom Interaction
		2.5.4. Light–Atom Hamiltonian
		2.5.5. Light–Atom Dynamics
		2.5.6. Rabi Oscillation
	2.6. Strong Light-Atom Interactions
		2.6.1. Light–Atom Interaction in Free Space
		2.6.2. Cavity Interactions
		2.6.3. Light–Atom Entanglement Inside a Cavity
	2.7. Two-photon Transitions in Three-Level Atoms
		2.7.1. Three-Level Atom
		2.7.2. Resonant Interaction
		2.7.3. Off-Resonant Raman Transition
	2.8. Dynamics of Density Operator
	2.9. Interaction of Light with Atoms in Free Space
		2.9.1. Schrödinger Picture
		2.9.2. Heisenberg Picture
		2.9.3. Four-Wave Mixing in Four-Level Systems
		2.9.4. Interaction of Atoms with Light Inside an Optical Resonator
3. Quantum Communication
	3.1. Quantum Key Distribution
		3.1.1. Binary Representation
		3.1.2. Cryptography
		3.1.4. Polarization Basis
		3.1.5. BB84 Realization Using Polarization Qubits
	3.2. Quantum Teleportation
		3.2.1. Teleportation Using Polarization Qubits
		3.2.2. Experimental Quantum Teleportation
	3.3. Quantum Optical Memory
		3.3.1. Light Storage Using EIT
		3.3.2. Principles of Atomic Frequency Comb Memory
		3.3.3. Light Storage Using Gradient Echo Memory
		3.3.4. Efficiency and Fidelity of a Quantum Memory or Communication Channel
		3.3.5. State Tomography
		3.3.6. Quantum Memory Platforms
		3.3.7. Memory Compatibility and Integration
	3.4. DLCZ Entanglement Distribution Protocol
		3.4.1. Duan–Lukin–Cirac–Zoller Proposal (2001)
		3.4.2. Probability and Noise
	3.5. Long-Distance Entanglement Distribution
		3.5.1. Direct Entanglement Distribution
		3.5.2. Quantum Repeaters Based on QMs
		3.5.3. Multiplexed Quantum Repeaters
	3.6. Quantum Optical Networks: Implementation and Applications
		3.6.1. Hybrid Quantum Optical Interface
		3.6.2. Routing Information in Multiplexed Networks
		3.6.3. Interfacing Spontaneous Sources with Disparate Memories
		3.6.4. Example: Memory-Based QKD
		3.6.5. A Quantum Network Example Consisting of Users, Servers, and Routers
Bibliography
Index