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Adaptive Techniques in Practical Quantum Key Distribution Adaptive Techniques in Practical Quantum Key Distribution by Wenyuan Wang A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Graduate Department of Physics University of Toronto c Copyright 2020 by Wenyuan Wang Abstract Adaptive Techniques in Practical Quantum Key Distribution Wenyuan Wang Doctor of Philosophy Graduate Department of Physics University of Toronto 2020 Quantum Key Distribution (QKD) can provide information-theoretically secure communications and is a strong candidate for the next generation of cryptography. However, in practice, the performance of QKD is limited by \practical imperfections" in realistic sources, channels, and detectors (such as multi- photon components or imperfect encoding from the sources, losses and misalignment in the channels, or dark counts in detectors). Addressing such practical imperfections is a crucial part of implementing QKD protocols with good performance in reality. There are two highly important future directions for QKD: (1) QKD over free space, which can allow secure communications between mobile platforms such as handheld systems, drones, planes, and even satellites, and (2) fibre-based QKD networks, which can simultaneously provide QKD service to numerous users at arbitrary locations. These directions are both highly promising, but so far they are limited by practical imperfections in the channels and devices, which pose huge challenges and limit their performance. In this thesis, we develop adaptive techniques with innovative protocol and algorithm design, as well as novel techniques such as machine learning, to address some of these key challenges, including (a) atmospheric turbulence in channels for free-space QKD, (b) asymmetric losses in channels for QKD network, and (c) efficient parameter optimization in real time, which is important for both free-space QKD and QKD networks. We believe that this work will pave the way to important implementations of free-space QKD and fibre-based QKD networks in the future. ii Acknowledgements First, I would like to sincerely thank my PhD supervisor, Prof. Hoi-Kwong Lo, who has led me into the world of academic research. His kind guidance, deep knowledge in the field, and tremendous patience were all indispensable to my being able to complete this program so smoothly and take my first step in a research career. I am deeply grateful for the very kind help he has provided over the many years, and for making the PhD program a very fruitful and pleasant journey for me. I would also like to thank Prof. Li Qian and Prof. Daniel James for kindly being on my PhD supervisory committee and helping me over the years. I have benefited greatly from Prof. Qian's countless helpful suggestions and comments on many projects, and have also very much enjoyed Prof. James' two graduate courses. I would also like to thank Prof. Aephraim Steinberg and Prof. John Sipe for being on my SGS defense committee, and my special thanks to Dr. Zhilian Yuan for kindly being my external examiner. I would also like to take this opportunity to thank the many people who have helped and supported me in my academic life and made many projects possible. Specifically, I would like to thank Prof. Feihu Xu, who has offered me much guidance and support when I started out in this field, come up with many brilliant ideas and suggestions, and collaborated with us closely over the many years, and Prof. Marcos Curty, for the kind help and instruction during our many pleasant collaboration/fruitful discussions. I would like to thank Dr. Chen Feng who has offered much help and guidance when I first visited the University of Toronto in 2014, when he patiently taught me about Error-Correction Codes when I was still a clueless beginner. I would like to thank Dr. Zhiyuan Tang for kindly introducing fellow students and me to the laboratory devices. I would also like to thank Prof. Zidan Wang and Prof. Francis Chin, for being the supervisors for my undergraduate research at the University of Hong Kong in 2014 and 2015 and first introducing me to hands-on research. Moreover, I would like to thank Dr. Bing Qi, Prof. George Siopsis, Prof. Norbert Lutkenhaus, Prof. Thomas Jennewein, Dr. Charles Lim, Dr. Koji Azuma, Prof. Kiyoshi Tamaki, Dr. Marco Lucamarini, Dr. Zhiliang Yuan, Dr. Cunlu Zhou, Prof. Xiongfeng Ma, Prof. Paul Kwiat for the help and insights over the collaborations and/or academic discussions. Also, I have benefited greatly from the many helpful discussions with and support from fellow stu- dents, including current and past fellow group members Olinka Bedroya, Xiaoqing Zhong, Chenyang Li, Eli Bourassa, Ilan Tzitrin, Michael Tisi, Reem Mandil, Yongtao Zhan, Amita Gnanapandithan, Thomas Van Himbeeck, and Anqi Mou, as well as friends from other research groups and other fields, including Chi Yan, Zihan Wang, Jie Luo, Jie Lin, Ian George, and Alistair Duff. Special thanks to Reem and Yongtao for their kind suggestions on my draft thesis. I would like to thank the support and funding of the University of Toronto Physics Department and thank the Natural Sciences and Engineering Research Council of Canada (NSERC), National Research Council of Canada (NRC), and U.S. Office of Naval Research (ONR) for funding several projects. I would like to thank Dr. Kevin McBryde and Dr. Stephen Hammel from U.S. SPAWAR Systems Center Pacific for kindly providing real-world atmospheric data and helpful discussions for the ONR project of QKD through turbulence. I'd also like to thank Nvidia and SciNet/Compute Canada for providing the computing equipment and services that supported many of the projects. Lastly, I would like to thank my family for all the love, support, and encouragement. I could not have been here without them. My parents' cultivation of my interest in science from a very young age, their selfless support, encouragement and guidance in my life, all make it possible for me to pursue my iii dream in the world of scientific research. This work is dedicated to the family I love, to the mentor I respect and look up to, and to the many people who have supported me on this path. iv Contents 1 Introduction 1 1.1 Quantum Key Distribution (QKD)...............................1 1.2 Motivation............................................3 1.2.1 Free-Space QKD.....................................3 1.2.2 Fibre-based Quantum Network.............................4 1.2.3 Machine Learning in QKD...............................5 1.3 Structure of Thesis........................................6 1.4 List of Publications and Presentations.............................7 1.4.1 Publications Included in this Thesis..........................7 1.4.2 Publications not Included in this Thesis........................7 1.4.3 Presentations.......................................8 2 Background on QKD Protocols9 2.1 List of Abbreviations.......................................9 2.2 BB84................................................ 10 2.3 Decoy-State Method....................................... 13 2.4 Measurement-Device-Independent (MDI) QKD........................ 15 2.4.1 Protocol.......................................... 15 2.4.2 Decoy-State MDI-QKD................................. 18 2.5 Twin-Field (TF) QKD...................................... 19 2.5.1 Motivation........................................ 19 2.5.2 Proposal of TF-QKD................................... 21 2.5.3 Variants of TF-QKD and Security Proofs....................... 22 2.6 Finite-Size Analysis....................................... 23 2.7 Parameter Optimization..................................... 25 3 BB84 over a Turbulent Free-Space Channel 28 3.1 Background............................................ 28 3.2 Methods.............................................. 30 3.2.1 The ARTS Method.................................... 30 3.2.2 General Framework for QKD Key Rate in a Turbulent Channel........... 31 3.2.3 Optimal Threshold and Near-Tightness of Upper Bound............... 34 3.2.4 Numerical Results.................................... 37 3.3 Decoy-State BB84........................................ 38 v 3.4 Decoy-State BB84 with Finite-size Effects........................... 39 3.5 Conclusion and Discussions................................... 41 4 MDI-QKD over Turbulent Free-Space Channels 44 4.1 Background............................................ 44 4.2 Theory............................................... 45 4.2.1 Channel Model under Turbulence............................ 46 4.2.2 Models for Key Rate................................... 48 4.2.3 Choice of Post-selection Thresholds........................... 50 4.3 Numerical Results........................................ 51 4.4 Discussions............................................ 52 5 MDI-QKD over Asymmetric Channels 53 5.1 Background............................................ 53 5.2 Asymmetric Protocols...................................... 56 5.2.1 Asymmetry between Bases in MDI-QKD....................... 57 5.2.2 Using Decoupled Bases and Asymmetric Intensities.................. 58 5.2.3 Security.......................................... 60 5.2.4 Parameter Optimization................................. 62 5.3 Simulation Results........................................ 65 5.4 Conclusion............................................ 69 6 TF-QKD over Asymmetric Channels 70 6.1 Background............................................ 70 6.2 Protocol.............................................. 71 6.3 Security.............................................. 73 6.4 Performance...........................................
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