This is an extremely clear, carefully written book that covers the most important results in the sprawling field of quantum information. It is perfect for a reference, self-study, or a graduate course in quantum information. It makes no attempt to be broad or encyclopedic, but instead goes deep into the core topics. The definitions and theorems are all precisely worded, and (starting in Chapter 2) all results have complete proofs, making the book largely self-contained. The book focuses heavily on the mathematical results and nuts-and-bolts techniques underpinning current research, and as such gives the reader a thorough and flexible toolkit for proving new results. If you are just looking for a broad but cursory survey of the field, then this is probably not the book for you. If, however, you want a working knowledge of the core results and proof techniques of quantum information with an eye toward doing cutting-edge research in the field, then this book will be an indispensable addition to your library.
The mathematical theory of quantum information studies the ultimate abilities and limits of transmitting and processing information using the laws of quantum mechanics. It owes much of its motivation to classical information theory, which was largely developed by Claude Shannon in the mid 20th century, and to quantum mechanics itself (of course). It addresses basic questions like: how much information can be transmitted through quantum channels, noisy or otherwise, and how entanglement helps. The theory informs, and is informed by, its sister disciplines of quantum computation and quantum communication (which overlap with physics and computer science), although in some sense it is more fundamental. Though he occasionally mentions applications to these other areas, Watrous seats his book squarely in the realm of pure mathematics.
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