Quantum information theory is at the frontiers of physics, mathematics and information science, offering a variety of solutions that are impossible using classical theory. This book provides an introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. After a gentle introduction to the necessary mathematics the authors describe the geometry of quantum state spaces. Focusing on finite dimensional Hilbert spaces, they discuss the statistical distance measures and entropies used in quantum theory. The final part of the book is devoted to quantum entanglement - a non-intuitive phenomenon discovered by Schrödinger, which has become a key resource for quantum computation. This richly-illustrated book is useful to a broad audience of graduates and researchers interested in quantum information theory. Exercises follow each chapter, with hints and answers supplied.
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.
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.
In The Entangled God, Kirk Wegter-McNelly addresses the age-old theological question of how God is present to the world by constructing a novel, scientifically informed account of the God–world relation. Drawing on recent scientific and philosophical work in "quantum entanglement," Wegter-McNelly develops the metaphor of "divine entanglement" to ground the relationality and freedom of physical process in the power of God’s relational being. The Entangled God makes a three-fold contribution to contemporary theological and religious discourse. First, it calls attention to the convergence of recent theology around the idea of "relationality." Second, it introduces theological and religious readers to the fascinating story of quantum entanglement. Third, it offers a robust "plerotic" alternative to kenotic accounts of God’s suffering presence in the world. Above all, this book takes us beyond the view of theology and science as adversaries and demonstrates the value of constructively relating these two important areas of intellectual investigation.
Das Buch bietet eine Einführung in die zum Studium der Theoretischen Physik notwendigen mathematischen Grundlagen. Der erste Teil des Buches beschäftigt sich mit der Theorie der Distributionen und vermittelt daneben einige Grundbegriffe der linearen Funktionalanalysis. Der zweite Teil baut darauf auf und gibt eine auf das Wesentliche beschränkte Einführung in die Theorie der linearen Operatoren in Hilbert-Räumen. Beide Teile werden von je einer Übersicht begleitet, die die zentralen Ideen und Begriffe knapp erläutert und den Inhalt kurz beschreibt. In den Anhängen werden einige grundlegende Konstruktionen und Konzepte der Funktionalanalysis dargestellt und wichtige Konsequenzen entwickelt.
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.
Der Weg zur Wirklichkeit ist eine Kurzübersetzung des Penrose-Klassikers "The Road to Reality", die aus dem Monumentalwerk für Physik- und Mathematikexperten die allgemeinverständlichen Kapitel für interessierte Laien lesbar macht. Wer ein Faible für die Grundfragen der Wissenschaft, einen Blick für Geometrie, einen Sinn für Zahlen und Neugier für kosmologische Theorien hat, findet in diesem klar und kompetent geschriebenen Buch überraschende und provozierende Ideen. Schulmathematik wie die Bruchrechnung oder der berühmte Pythagorassatz lassen sich auf dem Weg zur Wirklichkeit völlig neu entdecken - im Spannungsfeld zwischen platonischer Mathematik, physikalischer Welt und menschlichem Bewusstsein.
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.
Von den Grundlagen bis zur Streutheorie – das Wichtigste zur Quantenmechanik Die Quantenphysik ist ein zentrales und spannendes, wenn auch von vielen Schülern und Studenten ungeliebtes Thema der Physik. Aber keine Sorge! Steven Holzner erklärt Ihnen verständlich und lebendig, was Sie über Quantenphysik wissen müssen. Er erläutert die Grundlagen von Drehimpuls und Spin, gibt Ihnen Tipps, wie Sie komplexe Gleichungen lösen und nimmt den klassischen Problemen der Quantenphysik den Schrecken. Dabei arbeitet er mit Beispielen, die er ausführlich erklärt und gibt Ihnen so zusätzliche Sicherheit auf einem vor Unschärfen wimmelnden Feld.
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.
Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.
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.
Several years ago our statistical friends and relations introduced us to the work of Amari and Barndorff-Nielsen on applications of differential geometry to statistics. This book has arisen because we believe that there is a deep relationship between statistics and differential geometry and moreoever that this relationship uses parts of differential geometry, particularly its 'higher-order' aspects not readily accessible to a statistical audience from the existing literature. It is, in part, a long reply to the frequent requests we have had for references on differential geometry! While we have not gone beyond the path-breaking work of Amari and Barndorff Nielsen in the realm of applications, our book gives some new explanations of their ideas from a first principles point of view as far as geometry is concerned. In particular it seeks to explain why geometry should enter into parametric statistics, and how the theory of asymptotic expansions involves a form of higher-order differential geometry. The first chapter of the book explores exponential families as flat geometries. Indeed the whole notion of using log-likelihoods amounts to exploiting a particular form of flat space known as an affine geometry, in which straight lines and planes make sense, but lengths and angles are absent. We use these geometric ideas to introduce the notion of the second fundamental form of a family whose vanishing characterises precisely the exponential families.
This book treats the central physical concepts and mathematical techniques used to investigate the dynamics of open quantum systems. To provide a self-contained presentation the text begins with a survey of classical probability theory and with an introduction into the foundations of quantummechanics with particular emphasis on its statistical interpretation. The fundamentals of density matrix theory, quantum Markov processes and dynamical semigroups are developed. The most important master equations used in quantum optics and in the theory of quantum Brownian motion are applied to thestudy of many examples. Special attention is paid to the theory of environment induced decoherence, its role in the dynamical description of the measurement process and to the experimental observation of decohering Schrodinger cat states. The book includes the modern formulation of open quantum systems in terms of stochastic processes in Hilbert space. Stochastic wave function methods and Monte Carlo algorithms are designed and applied to important examples from quantum optics and atomic physics, such as Levy statistics in the lasercooling of atoms, and the damped Jaynes-Cummings model. The basic features of the non-Markovian quantum behaviour of open systems are examined on the basis of projection operator techniques. In addition, the book expounds the relativistic theory of quantum measurements and discusses several examplesfrom a unified perspective, e.g. non-local measurements and quantum teleportation. Influence functional and super-operator techniques are employed to study the density matrix theory in quantum electrodynamics and applications to the destruction of quantum coherence are presented. The text addresses graduate students and lecturers in physics and applied mathematics, as well as researchers with interests in fundamental questions in quantum mechanics and its applications. Many analytical methods and computer simulation techniques are developed and illustrated with the help ofnumerous specific examples. Only a basic understanding of quantum mechanics and of elementary concepts of probability theory is assumed.