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Developing many of the major, exciting, pre- and post-millennium developments from the ground up, this book is an ideal entry point for graduate students into quantum information theory. Significant attention is given to quantum mechanics for quantum information theory, and careful studies of the important protocols of teleportation, superdense coding, and entanglement distribution are presented. In this new edition, readers can expect to find over 100 pages of new material, including detailed discussions of Bell's theorem, the CHSH game, Tsirelson's theorem, the axiomatic approach to quantum channels, the definition of the diamond norm and its interpretation, and a proof of the Choi-Kraus theorem. Discussion of the importance of the quantum dynamic capacity formula has been completely revised, and many new exercises and references have been added. This new edition will be welcomed by the upcoming generation of quantum information theorists and the already established community of classical information theorists.
This largely self-contained book on the theory of quantum information focuses on precise mathematical formulations and proofs of fundamental facts that form the foundation of the subject. It is intended for graduate students and researchers in mathematics, computer science, and theoretical physics seeking to develop a thorough understanding of key results, proof techniques, and methodologies that are relevant to a wide range of research topics within the theory of quantum information and computation. The book is accessible to readers with an understanding of basic mathematics, including linear algebra, mathematical analysis, and probability theory. An introductory chapter summarizes these necessary mathematical prerequisites, and starting from this foundation, the book includes clear and complete proofs of all results it presents. Each subsequent chapter includes challenging exercises intended to help readers to develop their own skills for discovering proofs concerning the theory of quantum information. Tags
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This volume provides the reader with a comprehensive and up-to-date treatise positioned at the junction of the areas of Machine Learning (ML) and Granular Computing (GrC). ML offers a wealth of architectures and learning methods. Granular Computing addresses useful aspects of abstraction and knowledge representation that are of importance in the advanced design of ML architectures. In unison, ML and GrC support advances of the fundamental learning paradigm. As built upon synergy, this unified environment focuses on a spectrum of methodological and algorithmic issues, discusses implementations and elaborates on applications. The chapters bring forward recent developments showing ways of designing synergistic and coherently structured ML-GrC environment. The book will be of interest to a broad audience including researchers and practitioners active in the area of ML or GrC and interested in following its timely trends and new pursuits.