Masahito Hayashi - Böcker

This book explains the group representation theory for quantum theory in the language of quantum theory. As is well known, group representation theory is very strong tool for quantum theory, in particular, angular momentum, hydrogen-type Hamiltonian, spin-orbit interaction, quark model, quantum optics, and quantum information processing including quantum error correction. To describe a big picture of application of representation theory to quantum theory, the book needs to contain the following six topics, permutation group, SU(2) and SU(d), Heisenberg representation, squeezing operation, Discrete Heisenberg representation, and the relation with Fourier transform from a unified viewpoint by including projective representation. Unfortunately, although there are so many good mathematical books for a part of six topics, no book contains all of these topics because they are too segmentalized. Further, some of them are written in an abstract way in mathematical style and, often, thematerials are too segmented. At least, the notation is not familiar to people working with quantum theory.Others are good elementary books, but do not deal with topics related to quantum theory. In particular, such elementary books do not cover projective representation, which is more important in quantum theory. On the other hand, there are several books for physicists. However, these books are too simple and lack the detailed discussion. Hence, they are not useful for advanced study even in physics. To resolve this issue, this book starts with the basic mathematics for quantum theory. Then, it introduces the basics of group representation and discusses the case of the finite groups, the symmetric group, e.g. Next, this book discusses Lie group and Lie algebra. This part starts with the basics knowledge, and proceeds to the special groups, e.g., SU(2), SU(1,1), and SU(d). After the special groups, it explains concrete applications to physical systems, e.g., angular momentum, hydrogen-type Hamiltonian, spin-orbit interaction, and quark model. Then, it proceeds to the general theory for Lie group and Lie algebra. Using this knowledge, this book explains the Bosonic system, which has the symmetries of Heisenberg group and the squeezing symmetry by SL(2,R) and Sp(2n,R). Finally, as the discrete version, this book treats the discrete Heisenberg representation which is related to quantum error correction. To enhance readers' undersnding, this book contains 54 figures, 23 tables, and 111 exercises with solutions.

This book is the first one addressing quantum information from the viewpoint of group symmetry. This book treats optimal information processes including quantum state estimation, quantum state cloning, estimation of group action and quantum channel etc.

This book explains the group representation theory for quantum theory in the language of quantum theory.

This book is the first one addressing quantum information from the viewpoint of group symmetry. This book treats optimal information processes including quantum state estimation, quantum state cloning, estimation of group action and quantum channel etc.

Recently, the field of quantum computation and information has been developing through a fusion of results from various research fields in theoretical and practical areas. This book consists of the reviews of selected topics charterized by great progress and cover the field from theoretical areas to experimental ones. It contains fundamental areas, quantum query complexity, quantum statistical inference, quantum cloning, quantum entanglement, additivity. It treats three types of quantum security system, quantum public key cryptography, quantum key distribution, and quantum steganography. A photonic system is highlighted for the realization of quantum information processing.

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 testingand 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.

Recently, the field of quantum computation and information has been developing through a fusion of results from various research fields in theoretical and practical areas. This book consists of the reviews of selected topics charterized by great progress and cover the field from theoretical areas to experimental ones. It contains fundamental areas, quantum query complexity, quantum statistical inference, quantum cloning, quantum entanglement, additivity. It treats three types of quantum security system, quantum public key cryptography, quantum key distribution, and quantum steganography. A photonic system is highlighted for the realization of quantum information processing.

This book presents the basics of quantum information, e.g., foundation of quantum theory, quantum algorithms, quantum entanglement, quantum entropies, quantum coding, quantum error correction and quantum cryptography. As important quantum protocols, this book contains quantum teleportation, quantum dense coding, quantum data compression.

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.

This book presents the basics of quantum information, e.g., foundation of quantum theory, quantum algorithms, quantum entanglement, quantum entropies, quantum coding, quantum error correction and quantum cryptography. As important quantum protocols, this book contains quantum teleportation, quantum dense coding, quantum data compression.

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.