Quantum Information: An Introduction

Description

Recently, quantum information theory has been developing through a fusion of results from various research fields. This requires that understanding of basic results on diverse topics, and derived from different disciplinary perspectives, is required for appreciating the overall picture. Intended to merge key topics from both the information-theoretic and quantum- mechanical viewpoints, this graduate-level textbook provides a unified viewpoint of quantum information theory and lucid explanations of those basic results, so that the reader fundamentally grasps advances and challenges. For example, advanced topics in quantum communication such as quantum teleportation, superdense coding, quantum state transmission (quantum error-correction), and quantum encryption especially benefit from this unified approach. Unlike earlier treatments, the text requires knowledge of only linear algebra, probability theory, and quantum mechanics, while it treats the topics of quantum hypothesis testing and the discrimination of quantum states, and quantum channel coding (message transmission) with the minimal amount of math needed to convey their essence. Solving the more than 240 exercises provides readers with practice that not only enriches their knowledge of quantum information theory, but also can equip them with the techniques necessary for pursuing their own research in this field. Prologue....Pages 1-7 Mathematical Formulation of Quantum Systems....Pages 9-25 Information Quantities and Parameter Estimation in Classical Systems....Pages 27-67 Quantum Hypothesis Testing and Discrimination of Quantum States....Pages 69-91 Classical-Quantum Channel Coding (Message Transmission)....Pages 93-116 State Evolution and Trace-Preserving Completely Positive Maps....Pages 117-143 Quantum Information Geometry and Quantum Estimation....Pages 145-184 Quantum Measurements and State Reduction....Pages 185-206 Entanglement and Locality Restrictions....Pages 207-274 Analysis of Quantum Communication Protocols....Pages 275-320 Source Coding in Quantum Systems....Pages 321-346