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This book is designed to make accessible to nonspecialists the still evolving concepts of quantum mechanics and the terminology in which these are expressed. The opening chapters summarize elementary concepts of twentieth century quantum mechanics and describe the mathematical methods employed in the field, with clear explanation of, for example, Hilbert space, complex variables, complex vector spaces and Dirac notation, and the Heisenberg uncertainty principle. After detailed discussion of the Schrödinger equation, subsequent chapters focus on isotropic vectors, used to construct spinors, and on conceptual problems associated with measurement, superposition, and decoherence in quantum systems. Here, due attention is paid to Bell’s inequality and the possible existence of hidden variables. Finally, progression toward quantum computation is examined in detail: if quantum computers can be made practicable, enormous enhancements in computing power, artificial intelligence, and secure communication will result. This book will be of interest to a wide readership seeking to understand modern quantum mechanics and its potential applications.

Mathematics --- History of physics --- Mathematical physics --- Quantum mechanics. Quantumfield theory --- Computer. Automation --- quantumfysica --- quantumtheorie --- quantumcomputers --- wiskunde --- fysica --- anno 2000-2099

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In this essay collection, leading physicists, philosophers, and historians attempt to fill the empty theoretical ground in the foundations of information and address the related question of the limits to our knowledge of the world. Over recent decades, our practical approach to information and its exploitation has radically outpaced our theoretical understanding - to such a degree that reflection on the foundations may seem futile. But it is exactly fields such as quantum information, which are shifting the boundaries of the physically possible, that make a foundational understanding of information increasingly important. One of the recurring themes of the book is the claim by Eddington and Wheeler that information involves interaction and putting agents or observers centre stage. Thus, physical reality, in their view, is shaped by the questions we choose to put to it and is built up from the information residing at its core. This is the root of Wheeler’s famous phrase “it from bit.” After reading the stimulating essays collected in this volume, readers will be in a good position to decide whether they agree with this view.

Philosophy of science --- History of physics --- Spectrometric and optical chemical analysis --- Computer. Automation --- electron spin resonance spectre --- quantumcomputers --- wetenschapsfilosofie --- informatietechnologie --- fysica

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This textbook is the first one addressing quantum information from the viewpoint of group symmetry. Quantum systems have a group symmetrical structure. This structure enables to handle systematically quantum information processing. However, there is no other textbook focusing on group symmetry for quantum information although there exist many textbooks for group representation. After the mathematical preparation of quantum information, this book discusses quantum entanglement and its quantification by using group symmetry. Group symmetry drastically simplifies the calculation of several entanglement measures although their calculations are usually very difficult to handle. This book treats optimal information processes including quantum state estimation, quantum state cloning, estimation of group action and quantum channel etc. Usually it is very difficult to derive the optimal quantum information processes without asymptotic setting of these topics. However, group symmetry allows to derive these optimal solutions without assuming the asymptotic setting. Next, this book addresses the quantum error correcting code with the symmetric structure of Weyl-Heisenberg groups. This structure leads to understand the quantum error correcting code systematically. Finally, this book focuses on the quantum universal information protocols by using the group SU(d). This topic can be regarded as a quantum version of the Csiszar-Korner's universal coding theory with the type method. The required mathematical knowledge about group representation is summarized in the companion book, Group Representation for Quantum Theory.

Group theory --- Quantum mechanics. Quantumfield theory --- Spectrometric and optical chemical analysis --- Production management --- Computer. Automation --- quantumfysica --- electron spin resonance spectre --- quantumtheorie --- quantumcomputers --- veiligheid (mensen) --- klonen --- informatietechnologie --- wiskunde

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This book discusses modern approaches and challenges of computer-aided design (CAD) of quantum circuits with a view to providing compact representations of quantum functionality. Focusing on the issue of quantum functionality, it presents Quantum Multiple-Valued Decision Diagrams (QMDDs – a means of compactly and efficiently representing and manipulating quantum logic. For future quantum computers, going well beyond the size of present-day prototypes, the manual design of quantum circuits that realize a given (quantum) functionality on these devices is no longer an option. In order to keep up with the technological advances, methods need to be provided which, similar to the design and synthesis of conventional circuits, automatically generate a circuit description of the desired functionality. To this end, an efficient representation of the desired quantum functionality is of the essence. While straightforward representations are restricted due to their (exponentially) large matrix descriptions and other decision diagram-like structures for quantum logic suffer from not comprehensively supporting typical characteristics, QMDDs employ a decomposition scheme that more naturally models quantum systems. As a result, QMDDs explicitly support quantum-mechanical effects like phase shifts and are able to take more advantage of corresponding redundancies, thereby allowing a very compact representation of relevant quantum functionality composed of dozens of qubits. This provides the basis for the development of sophisticated design methods as shown for quantum circuit synthesis and verification.

Mathematical logic --- Algebra --- Quantum mechanics. Quantumfield theory --- Spectrometric and optical chemical analysis --- Computer architecture. Operating systems --- Computer. Automation --- algebra --- quantumfysica --- electron spin resonance spectre --- quantumtheorie --- quantumcomputers --- informatica --- informatietechnologie

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This graduate textbook provides a unified view of quantum information theory. Clearly explaining the necessary mathematical basis, it merges key topics from both information-theoretic and quantum- mechanical viewpoints and provides lucid explanations of the basic results. Thanks to this unified approach, it makes accessible such advanced topics in quantum communication as quantum teleportation, superdense coding, quantum state transmission (quantum error-correction) and quantum encryption. Since the publication of the preceding book Quantum Information: An Introduction, there have been tremendous strides in the field of quantum information. In particular, the following topics – all of which are addressed here – made seen major advances: quantum state discrimination, quantum channel capacity, bipartite and multipartite entanglement, security analysis on quantum communication, reverse Shannon theorem and uncertainty relation. With regard to the analysis of quantum security, the present book employs an improved method for the evaluation of leaked information and identifies a remarkable relation between quantum security and quantum coherence. Taken together, these two improvements allow a better analysis of quantum state transmission. In addition, various types of the newly discovered uncertainty relation are explained. Presenting a wealth of new developments, the book introduces readers to the latest advances and challenges in quantum information. To aid in understanding, each chapter is accompanied by a set of exercises and solutions.

Mathematics --- Mathematical physics --- Spectrometric and optical chemical analysis --- Information systems --- Computer. Automation --- ICT (informatie- en communicatietechnieken) --- electron spin resonance spectre --- quantumcomputers --- informatica --- informatiesystemen --- informatietechnologie --- wiskunde --- fysica