A Short Introduction to Quantum Information and Quantum Computation , Michel Le Bellac (translated from French by Patricia de Forcrand-Millard) Cambridge U. Press, New York, 2006. $60.00 (167 pp). ISBN 978-0-521-86056-7
As a researcher in quantum-information science, I have been paying a considerable amount of attention to the growing literature on the subject and how the science is being introduced to the broader community of physicists and physics students. In the past few years, the majority of the monographs on quantum-information science that have appeared have been short introductions to the field. Most of those texts, like Michel Le Bellac 's A Short Introduction to Quantum Information and Quantum Computation , are successful attempts to explain what physicists mean when they use the term “quantum information” and how information processing in quantum systems can be especially useful during an era in which nanotechnology is being developed.
The book introduces the qubit (quantum bit) and discusses the no-cloning theorem, the Bell inequalities, quantum teleportation, and dense coding. The author also sketches out a few of the genuinely quantum algorithms recently known to exist. About half of the recently published introductory texts provide fairly concrete examples of how quantum-information processing should be done in such settings as optics, nuclear magnetic resonance, ion traps, superconductors, and quantum dots. Le Bellac 's book, which first appeared in French in 2005, is clear in its presentations. Although A Short Introduction to Quantum Information and Quantum Computation originated in a course for computer scientists, it is well suited for physicists who hold at least a bachelor 's degree. For such readers, the book fully lives up to its name and is first-rate.
The key questions to be asked of an introductory text are whether a nonspecialist in quantum information could adopt it as an aid in research and whether an instructor could adopt it in the classroom. The benchmark text in this area is Michael Nielsen and Isaac Chuang 's Quantum Computation and Quantum Information (Cambridge U. Press, 2000), which contains almost 700 pages. The two books–-Nielsen and Chuang 's and Le Bellac's–-successfully serve researchers: They provide examples in a range of physical contexts, although Le Bellac 's book does so more efficiently.
However, in the context of an introductory class for nonspecialist students, Nielsen and Chuang 's excellent text can be a bit overwhelming. A majority of the recent monographs on quantum computing and quantum information, including Le Bellac's, have been much more modest in detail, replacing proof sketches with short, illuminating calculations. Those books typically leave out many of the subtler and foundational questions addressed by Nielsen and Chuang and by John Preskill 's quantum-computation lecture notes (1997–2004), which are freely accessible online at http://www.theory.caltech.edu/people/preskill/ph229/#lecture.
Although Le Bellac 's book does not delve much into foundational areas of the subject compared with the Nielson and Chuang or Preskill works, the text stands above other worthy introductory books, such as Quantum Approach to Informatics by Stig Stenholm and Kalle-Antti Suominen (Wiley-Interscience, 2005). Le Bellac accomplishes that by maintaining a close connection to physics as he covers most of the theoretical situations that are basic to quantum-information science instead of waiting until the end of the chapter to introduce physical examples. His approach is similar to that of Mladen Pavičić 's Quantum Computation and Quantum Communication: Theory and Experiments (Springer, 2006); Pavičić 's book, however, does not include exercises.
As a senior particle theorist at the Nonlinear Institute of Nice in France, Le Bellac has written several books, which appears to have helped him immensely in providing an accessible and physical primer to the subject, particularly for students and nonspecialists. A Short Introduction to Quantum Information and Quantum Computation is a laudable textbook by an author who has much experience writing about physics. It outperforms other similar texts that contain more pages but fail to communicate the essence of the subject to anyone not working in the field. The only small disappointment is the brevity of its bibliography, which includes fewer than 50 citations. On the other hand, Le Bellac 's book is designed as a self-contained, short introduction rather than a comprehensive overview of the subject. It fully succeeds in its mission.
