This is a book on the mathematical theory of quantum information, focusing
on a formal presentation of definitions, theorems, and proofs. It is primarily
intended for graduate students and researchers having some familiarity with
quantum information and computation, such as would be covered in an
introductory-level undergraduate or graduate course, or in one of several
books on the subject that now exist.
Quantum information science has seen an explosive development in recent
years, particularly within the past two decades. A comprehensive treatment
of the subject, even if restricted to its theoretical aspects, would certainly
require a series of books rather than just one. Consistent with this fact, the
selection of topics covered herein is not intended to be fully representative
of the subject. Quantum error correction and fault-tolerance, quantum
algorithms and complexity theory, quantum cryptography, and topological
quantum computation are among the many interesting and fundamental
topics found within the theoretical branches of quantum information science
that are not covered in this book. Nevertheless, one is likely to encounter
some of the core mathematical notions discussed in this book when studying
these topics.
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