книга Quantum Key Distribution: An Introduction with Exercises

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Quantum Key Distribution: An Introduction with Exercises

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Название: Quantum Key Distribution: An Introduction with Exercises
Автор: Ramona Wolf
Страниц: 235
Формат: PDF, EPUB
Размер: 10.7 MB
Качество: Отличное
Язык: Английский
Год издания: 2021

This textbook introduces the non-specialist reader to the concepts of quantum key distribution and presents an overview of state-of-the-art quantum communication protocols and applications. The field of quantum cryptography has advanced rapidly in the previous years, not least because with the age of quantum computing drawing closer, traditional encryption methods are at risk. The textbook presents the necessary mathematical tools without assuming much background, making it accessible to readers without experience in quantum information theory. 

In particular, the topic of classical and quantum entropies is presented in great detail. Furthermore, the author discusses the different types of quantum key distribution protocols and explains several tools for proving the security of these protocols. In addition, a number of applications of quantum key distribution are discussed, demonstrating its value to state-of-the-art cryptography and communication.

Quantum key distribution addresses one of the society’s most pressing concerns for secret and authenticated communication. This is achieved by exploiting the principles of quantum theory to establish a secret key between two distant parties whose security is guaranteed by the laws of physics. In the past years, there has been tremendous progress with regard to the design of novel protocols, the development of sophisticated techniques for security proofs, and even in-field implementations of technological prototypes.

The concept of private key cryptography is as old as the desire to exchange secret messages with others. A famous example of how cryptography has had an influence on the outcome of a war is how the British (most famously, Alan Turing) have cracked the Enigma code used by the Germans to communicate during World War II. Even more sophisticated schemes such as the Vigenere cipher, which could not be cracked for over three centuries, turned out to be not secure in the end: although the scheme to crack this cipher was more sophisticated than a simple frequency analysis, it was finally found. This shows an important point: people who use certain cryptographic schemes always have to be vigilant in case someone found a way to crack their scheme. We do not want to go into too much detail here, but one point should have become clear: there is a great desire for a cryptographic scheme that is unbreakable (or, in more technical terms, information-theoretically secure), even if an adversary had all the computational power in the universe.

This book leads the reader through the mathematical background with a variety of worked-out examples and exercises. It is primarily targeted at graduate students and advanced undergraduates in theoretical physics. The presented material is largely self-contained and only basic knowledge in quantum mechanics and linear algebra is required.


1. Introduction

1. 1 Classical Cryptography 1

1. 2 Provably Secure Cryptography 3

1. 3 The BB84 Protocol 7

1. 3. 1 Polarization of Photons 8

1. 3. 2 Quantum Transmission 9

1. 3. 3 Classical Post-Processing 9

1. 3. 4 Security of the BB84 Protocol 11

1. 4 Structure of the Book 11

2. Mathematical Tools

3. Information and Entropies

3. 1 Classical Entropies 53

3. 2 Quantum Entropies 72

4. Quantum Key Distribution Protocols

4. 1 Quantum Transmission 92

4. 2 Classical Post-Processing 107

5. Security Analysis

5. 1 Definition of Security 117

5. 2 Assumptions 124

5. 3 Eavesdropping Strategies 126

5. 3. 1 Classification of Attacks 127

5. 3. 2 Photon-Number-Splitting Attack 131

5. 4 Security of BB84 134

5. 4. 1 Security of the Entanglement-Based Version 135

5. 4. 2 Reduction to the Prepare-and-Measure Version 139

5. 5 Modern Techniques 144

5. 5. 1 The Secret Key Rate 144

5. 5. 2 Security from Entropic Uncertainty Relations 145

5. 6 Finite-Key Analysis 149

6. Device-Independent QKD

6. 1 Device-Independent Concepts 159

6. 1. 1 Black Boxes 159

6. 1. 2 Bell Inequalities 162

6. 1. 3 Motivation for Device-Independent QKD 165

6. 2 DIQKD Protocols and Security 167

6. 2. 1 Security Against Collective Attacks 167

6. 2. 2 Security Against Coherent Attacks 173

6. 2. 3 Modifications of the Protocol 175

6. 3 Loopholes 176

6. 3. 1 The Locality Loophole 176

6. 3. 2 The Detection Loophole 177

7. Recent Developments in Practical QKD

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