UNIVERSITE´ LIBRE DEBRUXELLES
Facult´e des Sciences Appliqu´ees
Information-Theoretic Aspects of Quantum Key Distribution
Th`ese pr´esent´ee par
Gilles V
ANA
SSCHE en vue de l’obtention du grade deDocteur en Sciences Appliqu´ees
Promoteur:
Prof. Nicolas C
ERFService de Th´eorie de l’Information et des Communications
Ann´ee acad´emique 2004-2005
2005-04-25 16:51
Contents
1 Introduction 11
1.1 A Bit of History . . . 11
1.2 Context of This Thesis . . . 13
1.3 Contributions . . . 14
2 Preliminaries 19 2.1 Cryptography . . . 19
2.2 Miscellaneous Discrete Concepts . . . 21
2.3 Classical Information Theory . . . 23
2.4 Quantum Information Theory . . . 28
2.5 Quantum Key Distribution . . . 34
3 Cryptosystems Based on Quantum Key Distribution 39 3.1 Confidentiality with the One-Time Pad . . . 39
3.2 The Classical Authenticated Channel . . . 40
3.3 The Source of Random Numbers . . . 43
3.4 A Secret-Key Encryption Scheme . . . 44
3.5 Combining Quantum and Classical Cryptography . . . 45
3.6 Implementation of a QKD-Based Cryptosystem . . . 48
3.7 Conclusion . . . 53
4 General Results on Secret-Key Distillation 55 4.1 A Two-Step Approach . . . 55
4.2 Characteristics of Distillation Techniques . . . 56
4.3 Authenticated One-Shot Secret-Key Distillation . . . 57
4.4 Authenticated Repetitive Secret-Key Distillation . . . 60
4.5 Unauthenticated Secret-Key Distillation . . . 63
4.6 Secret-Key Distillation with Continuous Variables . . . 64
4.7 Conclusion . . . 67
5 Privacy Amplification Using Families of Hash Functions 69 5.1 Requirements and Motivations . . . 69
5.2 Implementation of Hash Functions in a Binary Field . . . 73
5.3 New Families of Hash Functions . . . 75
5.4 Conclusion . . . 78
4 CONTENTS
6 Reconciliation 79
6.1 Problem Description . . . 79
6.2 Source Coding with Side Information . . . 82
6.3 Near-Lossless Unrestricted Inputs Codes . . . 88
6.4 Binary Interactive Error Correction Protocols . . . 95
6.5 Sliced Error Correction . . . 98
6.6 Reconciliation of Gaussian Key Elements . . . 106
6.7 Conclusion . . . 115
7 Protocols for Quantum Key Distribution with Continuous Variables 117 7.1 From Discrete to Continuous Variables . . . 117
7.2 A Protocol with Squeezed States . . . 118
7.3 A Protocol with Coherent States . . . 122
7.4 Implementation of a Protocol with Coherent States . . . 125
7.5 Conclusion . . . 132
8 Secret-Key Distillation and Quantum Key Distribution 133 8.1 Eavesdropping Strategies and Secret-Key Distillation . . . 133
8.2 Secret-Key Distillation Derived from Entanglement Purification 135 8.3 Application to a Protocol with Coherent States . . . 142
8.4 Conclusion . . . 163
9 Conclusion and Perspectives 165 A Joint Entropy-Constrained Multiterminal Quantization 169 A.1 Introduction . . . 169
A.2 Optimality Conditions . . . 170
A.3 Alternative Design . . . 171
A.4 Experiments . . . 172
A.5 Conclusion . . . 175
B Using XML for Better Content and Presentation Separation 177 B.1 Of Love and Hate . . . 177
B.2 XML for Scientific Documents . . . 178
B.3 From a Single Source to Multiple Targets . . . 179
B.4 Putting the Pieces Together . . . 179
B.5 Conclusion . . . 180
