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Quantum Information Theory
"We are the product of quantum fluctuations in the very early universe."
— Stephen Hawking
The modern field of quantum information theory contains numerous branches, including quantum foundations, quantum Shannon theory, various quantum protocols, and more. It also has overlapping connections with other areas of physics such as condensed matter physics, high energy physics, and quantum gravity.
Check this blog (link) for details of "PC5228 Quantum Information and Computation (2025 fall)" in NUS.
Check this blog (link) for details of "PC5228 Quantum Information and Computation (2024 fall)" in NUS. Also check this blog (link) for an older version.
An incomplete PDF version of lecture note that I wrote is here: link. Also check this link for a short PDF lecture note that Dag and I wrote.
Some general references
- John Preskill, Course Information for Physics 219/Computer Science 219 Quantum Computation (Formerly Physics 229)[link]. This page is a collection of wonderful lecture notes by Preskill on quantum information theory. In Fall 2020 his course is recoded, see the online videos Ph/CS 219A Quantum Computation.
- Michael A. Nielsen and Isaac L. Chuang, Quantum Computation and Quantum Information. This a standard textbook for quantum information and quantum computation theory.
- Mark Wilde, Quantum Information Theory. This book provides a comprehensive discussion of quantum Shannon theory, covering a wide range of topics in depth.
- John Watrous, The Theory of Quantum Information. This is a book that contains many mathematical details on techniques used in quantum informtaion theory. His Theory of Quantum Information and Advanced topics in Quantum Information Theory are also very good reading materials.
- Vlako Vedral, Introduction to quantum information science, this book covers the basics of quantum information theory and quantum computation theory.
- Denes Petz, Quantum Information Theory and Quantum Statistics, leans more towards a mathematician-oriented approach. It covers several topics that are typically not addressed in standard quantum information textbooks.
- Sumeet Khatri and Mark M. Wilde, Principles of Quantum Communication Theory: A Modern Approach, the pdf version is avaliable on arxiv: 2011.04672. This 1,240-page book covers numerous topics on quantum communications that are rarely found elsewhere.
- Gregg Jaeger, Quantum Information-An Overview. This is a concise book that serves as a good introduction for beginners.
- Giuliano Benenti, Giulio Casati, and Giuliano Strini’s Principles of Quantum Computation and Information Volumes I & II are excellent resources for beginners.
- Karl Kraus, States, Effects, and Operations: Fundamental Notions of Quantum Theory, published in 1983, may not be considered an ideal textbook today. However, I will mention it for readers interested in the history of quantum information.
- Asher Peres, Quantum Theory: Concepts and Methods is another classic book that explores many fascinating topics in the foundations of quantum theory.
If you like mathematics related to quantum information theory, I would like to recommend (notice that to read these books, you should have some background on analysis and topology first):
- Guillaume Aubrun, Alice and Bob Meet Banach: The Interface of Asymptotic Geometric Analysis and Quantum Information Theory. This book is a discussion of quantum information theory from functional analysis perspective.
- Vern Paulsen, Completely Bounded Maps and Operator Algebras. This book covers many crurical results for us to understand CP maps, channels, etc., from the mathematical perspective.
- Charalambos D. Aliprantis , Owen Burkinshaw, Positive Operators. As it name indicated, this is a book about positive operators.
- R. Tyrrell Rockafellar, Convex Analysis. This is a classics about convex analysis, you will encounter convex analysis in many places of quantum information theory.
- Rajendra Bhatia, Matrix analysi, this from famous GMT series. Matrix analysis plays a crucial role in quantum information theory.