geometry of quantum states an introduction to quantum entanglement

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Geometry Of Quantum States

Author : Ingemar Bengtsson
ISBN : 9781108293495
Genre : Science
File Size : 32. 33 MB
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Quantum information theory is a branch of science at the frontier of physics, mathematics, and information science, and offers a variety of solutions that are impossible using classical theory. This book provides a detailed introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. The second edition contains new sections and entirely new chapters: the hot topic of multipartite entanglement; in-depth discussion of the discrete structures in finite dimensional Hilbert space, including unitary operator bases, mutually unbiased bases, symmetric informationally complete generalized measurements, discrete Wigner function, and unitary designs; the Gleason and Kochen–Specker theorems; the proof of the Lieb conjecture; the measure concentration phenomenon; and the Hastings' non-additivity theorem. This richly-illustrated book will be useful to a broad audience of graduates and researchers interested in quantum information theory. Exercises follow each chapter, with hints and answers supplied.

Geometry Of Quantum States An Introduction To Quantum Entanglement

Author : CTI Reviews
ISBN : 9781467204415
Genre : Education
File Size : 25. 6 MB
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Facts101 is your complete guide to Geometry of Quantum States, An Introduction to Quantum Entanglement. In this book, you will learn topics such as as those in your book plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.

Measuring The Quantum State Of Light

Author : Ulf Leonhardt
ISBN : 0521497302
Genre : Science
File Size : 46. 32 MB
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Appendix A: Semiclassical approximation

Geometric Phases In Classical And Quantum Mechanics

Author : Dariusz Chruscinski
ISBN : 081764282X
Genre : Mathematics
File Size : 88. 81 MB
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Several well-established geometric and topological methods are used in this work in an application to a beautiful physical phenomenon known as the geometric phase. This book examines the geometric phase, bringing together different physical phenomena under a unified mathematical scheme. The material is presented so that graduate students and researchers in applied mathematics and physics with an understanding of classical and quantum mechanics can handle the text.

Analytic Hyperbolic Geometry And Albert Einstein S Special Theory Of Relativity

Author : Abraham A. Ungar
ISBN : 9789812772299
Genre : Science
File Size : 72. 48 MB
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This book presents a powerful way to study Einstein's special theory of relativity and its underlying hyperbolic geometry in which analogies with classical results form the right tool. It introduces the notion of vectors into analytic hyperbolic geometry, where they are called gyrovectors. Newtonian velocity addition is the common vector addition, which is both commutative and associative. The resulting vector spaces, in turn, form the algebraic setting for the standard model of Euclidean geometry. In full analogy, Einsteinian velocity addition is a gyrovector addition, which is both gyrocommutative and gyroassociative. The resulting gyrovector spaces, in turn, form the algebraic setting for the Beltrami–Klein ball model of the hyperbolic geometry of Bolyai and Lobachevsky. Similarly, Mצbius addition gives rise to gyrovector spaces that form the algebraic setting for the Poincarי ball model of hyperbolic geometry. In full analogy with classical results, the book presents a novel relativistic interpretation of stellar aberration in terms of relativistic gyrotrigonometry and gyrovector addition. Furthermore, the book presents, for the first time, the relativistic center of mass of an isolated system of noninteracting particles that coincided at some initial time t = 0. The novel relativistic resultant mass of the system, concentrated at the relativistic center of mass, dictates the validity of the dark matter and the dark energy that were introduced by cosmologists as ad hoc postulates to explain cosmological observations about missing gravitational force and late-time cosmic accelerated expansion. The discovery of the relativistic center of mass in this book thus demonstrates once again the usefulness of the study of Einstein's special theory of relativity in terms of its underlying analytic hyperbolic geometry.

Coherent States Wavelets And Their Generalizations

Author : Syed Twareque Ali
ISBN : 9781461485353
Genre : Science
File Size : 80. 57 MB
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This second edition is fully updated, covering in particular new types of coherent states (the so-called Gazeau-Klauder coherent states, nonlinear coherent states, squeezed states, as used now routinely in quantum optics) and various generalizations of wavelets (wavelets on manifolds, curvelets, shearlets, etc.). In addition, it contains a new chapter on coherent state quantization and the related probabilistic aspects. As a survey of the theory of coherent states, wavelets, and some of their generalizations, it emphasizes mathematical principles, subsuming the theories of both wavelets and coherent states into a single analytic structure. The approach allows the user to take a classical-like view of quantum states in physics. Starting from the standard theory of coherent states over Lie groups, the authors generalize the formalism by associating coherent states to group representations that are square integrable over a homogeneous space; a further step allows one to dispense with the group context altogether. In this context, wavelets can be generated from coherent states of the affine group of the real line, and higher-dimensional wavelets arise from coherent states of other groups. The unified background makes transparent an entire range of properties of wavelets and coherent states. Many concrete examples, such as coherent states from semisimple Lie groups, Gazeau-Klauder coherent states, coherent states for the relativity groups, and several kinds of wavelets, are discussed in detail. The book concludes with a palette of potential applications, from the quantum physically oriented, like the quantum-classical transition or the construction of adequate states in quantum information, to the most innovative techniques to be used in data processing. Intended as an introduction to current research for graduate students and others entering the field, the mathematical discussion is self-contained. With its extensive references to the research literature, the first edition of the book is already a proven compendium for physicists and mathematicians active in the field, and with full coverage of the latest theory and results the revised second edition is even more valuable.

Noncommutative Geometry And Optimal Transport

Author : Pierre Martinetti
ISBN : 9781470422974
Genre : Mathematical optimization
File Size : 72. 9 MB
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The distance formula in noncommutative geometry was introduced by Connes at the end of the 1980s. It is a generalization of Riemannian geodesic distance that makes sense in a noncommutative setting, and provides an original tool to study the geometry of the space of states on an algebra. It also has an intriguing echo in physics, for it yields a metric interpretation for the Higgs field. In the 1990s, Rieffel noticed that this distance is a noncommutative version of the Wasserstein distance of order 1 in the theory of optimal transport. More exactly, this is a noncommutative generalization of Kantorovich dual formula of the Wasserstein distance. Connes distance thus offers an unexpected connection between an ancient mathematical problem and the most recent discovery in high energy physics. The meaning of this connection is far from clear. Yet, Rieffel's observation suggests that Connes distance may provide an interesting starting point for a theory of optimal transport in noncommutative geometry. This volume contains several review papers that will give the reader an extensive introduction to the metric aspect of noncommutative geometry and its possible interpretation as a Wasserstein distance on a quantum space, as well as several topic papers.

The Subtle Body

Author : Cyndi Dale
ISBN : 9781591798279
Genre : Body, Mind & Spirit
File Size : 42. 71 MB
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Welcome to the first comprehensive encyclopedia of the human energetic anatomy. Here is a reference that no personal or professional health-care library should be without—an in-depth, illustrated guide to the invisible energies of the spirit, psyche, and consciousness that influence every aspect of our well-being. Whether you are looking for the right complementary medicine to enhance your own healing practice, seeking perennial wisdom about your body’s energetic nature from world traditions, or exploring the quantum edge of intention-based care, The Subtle Body is an indispensible companion for exploring virtually any facet of holistic healing. Created for healing professionals and patients alike, this volume provides a lexicon of terms, illustrations, and detailed entries about our energetic biology and how it relates to our physical being. This invaluable information will help you enhance any form of health care and give you the knowledge you need to develop an integrated approach for your clients’ well-being—or your own. All healers are "energetic" healers, whether they know it or not. Because every health issue has a physical and an energetic component, even a simple physical treatment like bandaging a cut also impacts the body's spiritual, mental, and emotional welfare. The Subtle Body is a comprehensive encyclopedia devoted to the critical world of our invisible anatomy, where so much of healing actually occurs. Compiled by intuitive healer and scholar Cyndi Dale, this 500-page full color illustrated reference book covers: What is the "subtle body"? New scientific understanding of our quantum-state existence and the unseen fields that determine our physical condition True integrative care: how combining Eastern energetic modalities with Western scientific rigor yields optimum results The meridians, fields, and chakras: detailed information and diagrams about the role of these energetic structures in our overall health Energy-based therapy principles from the world's healing traditions--including Ayurveda, Qigong, Reiki, Quabalah, and many more For professionals who want to make the leap from being good healers to great ones, one thing is clear: we need to care for every facet of our well-being. With The Subtle Body, practitioners and patients alike now have an unprecedented resource for understanding the physical, energetic, and spiritual elements of human health--for an informed, complete approach to healing.

Quantum Information

Author : Masahito Hayashi
ISBN : 9783540302650
Genre : Science
File Size : 31. 12 MB
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This graduate-level textbook provides a unified viewpoint of quantum information theory that merges key topics from both the information-theoretic and quantum- mechanical viewpoints. The text provides a unified viewpoint of quantum information theory and lucid explanations of those basic results, so that the reader fundamentally grasps advances and challenges. This unified approach makes accessible such advanced topics in quantum communication as quantum teleportation, superdense coding, quantum state transmission (quantum error-correction), and quantum encryption.

Quantum Signatures Of Chaos

Author : Fritz Haake
ISBN : 3540677232
Genre : Science
File Size : 50. 15 MB
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This textbook provides an excellent introduction to a new and rapidly developing field of research. Now well established as a textbook in this rapidly developing field of research, the new edition is much enlarged and covers a host of new results.

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