Information theory is a well-known field of study that in no small measure underlies the modern revolution in communication technologies. It famously grew out of Shannon’s singular 1948 paper [1] that established the core principles and results, namely, the entropy of a system, Shannon’s source coding theorem, and Shannon’s channel capacity theorem. Information theory uses probability theory and continuous (rather than discrete) mathematics for the most part, and also connects with diverse subjects such as physics (specifically, the second law of thermodynamics) and computability theory (specifically, Chaitin’s generalization of Gödel’s first incompleteness theorem).
Quantum theory is an area of physics that grew out of the seminal works of Max Planck, Schrödinger, and others, around the turn of the previous century. It enabled physicists to explain, among other things, the formerly incomprehensible constancy of the speed of light as observed by the Michelson–Morley experiment, and laid the foundation for further advances such as Einstein’s explanation of the photoelectric effect (and also, of course, his theory of relativity).
It was the physicist Feynman (who won a Nobel Prize for his work in quantum electrodynamics) who suggested, in the 1980s, that quantum-theoretic devices could be used for computation. This gave rise to the field of quantum computing. As an analog, we also have quantum information theory, with the latter being concerned with information transfer on quantum channels rather than conventional ones (with computation at the source as well as destination being assumed to be free and abundant). Though quantum computing and quantum information theory are yet to be realized in practical settings on a commercial scale, it is hoped that the ongoing century will see rapid advances that make them viable for widespread use. Such hope underlies the massive amount of theoretical work that has been carried out by researchers in these areas.
This book thus finds its place as a good reference work on quantum information theory (or what its author prefers to call quantum Shannon theory) that is sure to be welcomed by readers interested in its topic. The book gives a collected and sensibly organized presentation of results that are scattered about in dozens of papers published over the last few decades. It consists of 25 chapters divided into six parts. Part 1, an introduction, consists of two chapters that summarize basic concepts in quantum Shannon theory and give a somewhat more detailed overview of classical Shannon theory. Part 2 presents a summary, in three chapters, of quantum theory, not so much in a manner that would please a physicist, but more in a way that is appropriate given the scope of this book. The three chapters that make up Part 3 present basic concepts of quantum channels and protocols. In Part 4, the author covers the important results of quantum Shannon theory in significant mathematical depth (summarizing recent and ongoing research) in eight chapters. Part 5 deals with noiseless quantum Shannon theory in two chapters, and Part 6 with noisy quantum Shannon theory in seven chapters. There are two appendices that contain some basic mathematical background.
Though the primary readership of the book is presumably graduate students and researchers who are hardcore theoreticians interested in a thorough study of its subject, it may also be of some use to practitioners and others who wish to glean insights on specific topics without necessarily getting too deep. However, though the author avers that he has taught this material to students (covering most of the book in one semester, though a more comfortable pace would require a two-semester sequence), instructors who wish to use this as a textbook would need to do their own work to prepare student exercises and other supplementary material (though the notes for further reading after each chapter are useful, as is the extensive bibliography at the end of the book).
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