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arXiv:2311.12442

Quantum Information Theory -- Lecture Notes

Christoph Dittel

Published Nov 21, 2023• 0 citations
arXivHTMLPDF

Abstract

These lecture notes provide an introduction to quantum information and quantum computation, which are strongly related disciplines and subject of intense research. The lecture notes contain only a small selection of topics in these disciplines, with the aim of providing you with an overview and a basic introduction. The corresponding lecture series is available on my YouTube channel.

DOI
10.48550/arxiv.2311.12442

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These lecture notes provide an introduction to quantum information and quantum computation, which are strongly related disciplines and subject of intense research. The lecture notes contain only a small selection of topics in these disciplines, with the aim of providing you with an overview and a basic introduction. The corresponding lecture series is available on my YouTube channel.
From the Publisher: This book aims to provide a pedagogical introduction to the subjects of quantum information and computation. Topics include non-locality of quantum mechanics, quantum computation, quantum cryptography, quantum error correction, fault-tolerant quantum computation as well as some experimental aspects of quantum computation and quantum cryptography. Only knowledge of basic quantum mechanics is assumed. Whenever more advanced concepts and techniques are used, they are introduced carefully. This book is meant to be a self-contained overview. While basic concepts are discussed in detail, unnecessary technical details are excluded. It is well-suited for a wide audience ranging from physics graduate students to advanced researchers.
Why yet another book on quantum information theory? Like many lecturers we began writing this text because none of the alternatives seemed quite right. This book is aimed squarely at undergraduate physics students who want a brief but reasonably thorough introduction to the exciting ideas of quantum information, including its applications in computation and communication. It is based on a short course we have taught to fourth-year students at Oxford University since 2004; for the most part it only assumes knowledge of elementary quantum mechanics and linear algebra, and so could even be taught to third-year undergraduates. A brief revision guide to quantum mechanics is provided as an appendix, which should cover any minor points that have been missed. As the title implies the book is structured in three parts, starting with the basics of quantum information and then applying this to quantum computation and quantum communication. Part I is self-contained, but contains only the barest hints of the exciting applications which attract many people to this field and so might prove unsatisfying on its own. Parts II and III draw heavily on Part I, but are largely independent of each other, and it would be perfectly possible to study only one of these two without the other. As this text is aimed at physics undergraduates, we believe that it is vital to cover experimental techniques, rather than merely presenting quantum information as a series of abstract quantum operations. We have, however, concentrated on the basic ideas underlying each approach, rather than worrying about particular experimental details.
Quantum information is an emerging field which has attracted a lot of attention in the last fifteen years or so. It is a broad subject which covers from the most applied questions (e.g., how to build quantum computers or secure cryptographic systems), to the most theoretical problems concerning the formalism of quantum mechanics, its complexity, and its potential to go beyond classical physics. I have written these notes as an introduction to the formalism of quantum information, trying to show how it is a natural progression from an undergraduate course on quantum mechanics (just as I felt it was for me). Hence, these are mainly notes about the language of quantum information and the meaning of its terms, not about its applications. They do not intend to be an exhaustive review about the field, but just a logical sequence of ideas, concepts and definitions, building up towards the continuous variables formalism, which actually takes over most of the notes. In this way, most of the results are stated without proof, and I haven't been careful with references; this is a work in progress, and I intend to add such things in the future. In any case, most of the topics that I introduce have been thoroughly covered in previous books and reviews, and with this notes I only intend to give my point of view, as well as to introduce the different topics and objects in exactly the way I work with and think about them, hoping it will be useful, especially for the people who are starting in the field. These notes originated in 2010 as a way of studying for my close collaboration with Raúl García-Patrón and Nicolas J. Cerf, to whom I am deeply grateful for guidance and incredibly clarifying discussions. They benefited greatly as well from the weeks I spent in Doha with Hyunchul Nha and his group in 2012, especially from discussions with him and Ho-Joon Kim.