Quantum Key Distribution: An Introduction with Exercises (Lecture Notes in Physics)

Preface
	Acknowledgements
Contents
About the Author
1 Introduction
	1.1 Classical Cryptography
	1.2 Provably Secure Cryptography
	1.3 The BB84 Protocol
		1.3.1 Polarization of Photons
		1.3.2 Quantum Transmission
		1.3.3 Classical Post-Processing
		1.3.4 Security of the BB84 Protocol
	1.4 Structure of the Book
	References
2 Mathematical Tools
	2.1 Basics in Linear Algebra
		2.1.1 The Hilbert Space
		2.1.2 Operators on Hilbert Spaces
		2.1.3 Composite Systems
	2.2 Description of Quantum Systems
		2.2.1 States in Hilbert Space
		2.2.2 Quantum Channels
		2.2.3 Measurements
	2.3 Composite Systems and Entanglement
		2.3.1 States in Composite Systems
		2.3.2 Entanglement
		2.3.3 Quantum–Classical Ensemble
		2.3.4 Evolution of Composite Systems
	2.4 The No-Cloning Theorem
	2.5 Purification
	2.6 Distance Measures
	References
3 Information and Entropies
	3.1 Classical Entropies
		3.1.1 Mathematical Properties
		3.1.2 Conditional Entropy
		3.1.3 Joint Entropy
		3.1.4 Mutual Information
		3.1.5 Relative Entropy
	3.2 Quantum Entropies
		3.2.1 Mathematical Properties of Quantum Entropy
		3.2.2 Joint Quantum Entropy
		3.2.3 Conditional Quantum Entropy
		3.2.4 Quantum Mutual Information
		3.2.5 Quantum Relative Entropy
		3.2.6 One-Shot Entropies
	3.3 The Entropic Uncertainty Principle
	References
4 Quantum Key Distribution Protocols
	4.1 Quantum Transmission
		4.1.1 Prepare-and-Measure Protocols
			4.1.1.1 The BB84 Protocol
			4.1.1.2 The Six-State Protocol
			4.1.1.3 The SARG04 Protocol
		4.1.2 Entanglement-Based Protocols
			4.1.2.1 The Ekert Protocol
			4.1.2.2 Entanglement-Based Version of BB84
		4.1.3 From Prepare-and-Measure to Entanglement-Based Protocols
	4.2 Classical Post-Processing
		4.2.1 Parameter Estimation
		4.2.2 Error Correction
		4.2.3 Privacy Amplification
	References
5 Security Analysis
	5.1 Definition of Security
	5.2 Assumptions
	5.3 Eavesdropping Strategies
		5.3.1 Classification of Attacks
		5.3.2 Photon-Number-Splitting Attack
	5.4 Security of BB84
		5.4.1 Security of the Entanglement-Based Version
		5.4.2 Reduction to the Prepare-and-Measure Version
	5.5 Modern Techniques
		5.5.1 The Secret Key Rate
		5.5.2 Security from Entropic Uncertainty Relations
	5.6 Finite-Key Analysis
	References
6 Device-Independent QKD
	6.1 Device-Independent Concepts
		6.1.1 Black Boxes
		6.1.2 Bell Inequalities
		6.1.3 Motivation for Device-Independent QKD
	6.2 DIQKD Protocols and Security
		6.2.1 Security Against Collective Attacks
		6.2.2 Security Against Coherent Attacks
		6.2.3 Modifications of the Protocol
	6.3 Loopholes
		6.3.1 The Locality Loophole
		6.3.2 The Detection Loophole
	References
7 Recent Developments in Practical QKD
	7.1 Practical Challenges in QKD
	7.2 Measurement Device-Independent QKD
		7.2.1 Detector Side Channel Attacks
		7.2.2 Practical MDI QKD
		7.2.3 Twin-Field QKD
	7.3 Continuous-Variable QKD
		7.3.1 Basics of Gaussian Quantum Information
		7.3.2 CV QKD Protocols
		7.3.3 Security Analysis
		7.3.4 Advantages and Challenges
	7.4 Advances in Experimental QKD
	References
A Basic Probability Theory
B Calderbank–Shor–Steane Codes
	B.1 Classical Linear Codes
	B.2 Quantum Error Correction
Index