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Entropy in Foundations of Quantum Physics by Marcin Pawłowski Pdf
This book is a collection of outstanding papers on various aspects of entropy at the foundation of quantum physics. The covered topics range from purely foundational issues such as contextuality and Bell and Leggett–Garg inequalities to applications such as quantum key distribution, teleportation, and image encoding. The main ingredient binding them together in this book is that in all of the contained papers, entropy plays a key role either as a mathematical tool or as a link which bridges the gap between different fields of science.
Entropy in Foundations of Quantum Physics by Marcin Pawłowski Pdf
This book is a collection of outstanding papers on various aspects of entropy at the foundation of quantum physics. The covered topics range from purely foundational issues such as contextuality and Bell and Leggett-Garg inequalities to applications such as quantum key distribution, teleportation, and image encoding. The main ingredient binding them together in this book is that in all of the contained papers, entropy plays a key role either as a mathematical tool or as a link which bridges the gap between different fields of science.
Quantum Information Processing with Finite Resources by Marco Tomamichel Pdf
This book provides the reader with the mathematical framework required to fully explore the potential of small quantum information processing devices. As decoherence will continue to limit their size, it is essential to master the conceptual tools which make such investigations possible. A strong emphasis is given to information measures that are essential for the study of devices of finite size, including Rényi entropies and smooth entropies. The presentation is self-contained and includes rigorous and concise proofs of the most important properties of these measures. The first chapters will introduce the formalism of quantum mechanics, with particular emphasis on norms and metrics for quantum states. This is necessary to explore quantum generalizations of Rényi divergence and conditional entropy, information measures that lie at the core of information theory. The smooth entropy framework is discussed next and provides a natural means to lift many arguments from information theory to the quantum setting. Finally selected applications of the theory to statistics and cryptography are discussed. The book is aimed at graduate students in Physics and Information Theory. Mathematical fluency is necessary, but no prior knowledge of quantum theory is required.
John von Neumann and the Foundations of Quantum Physics by Miklós Rédei,Michael Stöltzner Pdf
John von Neumann (1903-1957) was undoubtedly one of the scientific geniuses of the 20th century. The main fields to which he contributed include various disciplines of pure and applied mathematics, mathematical and theoretical physics, logic, theoretical computer science, and computer architecture. Von Neumann was also actively involved in politics and science management and he had a major impact on US government decisions during, and especially after, the Second World War. There exist several popular books on his personality and various collections focusing on his achievements in mathematics, computer science, and economy. Strangely enough, to date no detailed appraisal of his seminal contributions to the mathematical foundations of quantum physics has appeared. Von Neumann's theory of measurement and his critique of hidden variables became the touchstone of most debates in the foundations of quantum mechanics. Today, his name also figures most prominently in the mathematically rigorous branches of contemporary quantum mechanics of large systems and quantum field theory. And finally - as one of his last lectures, published in this volume for the first time, shows - he considered the relation of quantum logic and quantum mechanical probability as his most important problem for the second half of the twentieth century. The present volume embraces both historical and systematic analyses of his methodology of mathematical physics, and of the various aspects of his work in the foundations of quantum physics, such as theory of measurement, quantum logic, and quantum mechanical entropy. The volume is rounded off by previously unpublished letters and lectures documenting von Neumann's thinking about quantum theory after his 1932 Mathematical Foundations of Quantum Mechanics. The general part of the Yearbook contains papers emerging from the Institute's annual lecture series and reviews of important publications of philosophy of science and its history.
Quantum Foundations by Pedro W. Lamberti,Gustavo M. Bosyk,Sebastian Fortin,Federico Holik Pdf
Since its conception 90 years ago, the quantum uncertainty principle introduced by Werner Heisenberg lies behind most important features of quantum physics, and its implications have an impact that goes far beyond the physics community. This book focuses on the quantum uncertainty principle, providing an up-to-date examination of recent developments of its applications in quantum information theory. The book brings together several renowned experts working in the foundations of quantum mechanics and quantum information theory. The authors provide different approaches to the study of uncertainty relations and other fundamental aspects of the quantum formalism. Topics addressed include entanglement and Bell inequalities, the application of entropic information measures to the study of uncertainty inequalities, the characterization of deep learning networks in the context of adiabatic quantum computation, and the study of general properties of the set of quantum states. The content of this book will surely benefit both experienced and new researchers specializing in quantum information theory and the foundations of quantum mechanics.
Quantum Information and Foundations by Giacomo Mauro D’Ariano,Paolo Perinotti Pdf
Quantum information has dramatically changed information science and technology, looking at the quantum nature of the information carrier as a resource for building new information protocols, designing radically new communication and computation algorithms, and ultra-sensitive measurements in metrology, with a wealth of applications. From a fundamental perspective, this new discipline has led us to regard quantum theory itself as a special theory of information, and has opened routes for exploring solutions to the tension with general relativity, based, for example, on the holographic principle, on non-causal variations of the theory, or else on the powerful algorithm of the quantum cellular automaton, which has revealed new routes for exploring quantum fields theory, both as a new microscopic mechanism on the fundamental side, and as a tool for efficient physical quantum simulations for practical purposes. In this golden age of foundations, an astonishing number of new ideas, frameworks, and results, spawned by the quantum information theory experience, have revolutionized the way we think about the subject, with a new research community emerging worldwide, including scientists from computer science and mathematics.
New Foundations of Quantum Mechanics by Alfred Lande Pdf
Originally published in 1965, the aim of this book was to challenge the dualistic view of physics, that is, the assumption that beams of electrons consist of discrete particles and of waves. Lande argues that this dualistic view is unnecessary, not only on methodological grounds but also from the standpoint of physics. Lande sets out to point out that there are faults in the purely physical arguments, which have led to the dualistic doctrine and shows that by making use of the quantum rule for the exchange of linear momentum, established by W. Duane in 1923, wave-like phenomena can be fully explained on a unitary particle theory of matter. Chapters cover a variety of subjects and range from 'Dualism versus quantum mechanics' to the 'Origin of the quantum rules'. Appendices are included for reference. This book will be of value to students and scholars of the history of physics.
Author : Herbert S. Green Publisher : Springer Science & Business Media Page : 248 pages File Size : 55,5 Mb Release : 2012-12-06 Category : Science ISBN : 9783642571626
Information Theory and Quantum Physics by Herbert S. Green Pdf
In this highly readable book, H.S. Green, a former student of Max Born and well known as an author in physics and in the philosophy of science, presents a timely analysis of theoretical physics and related fundamental problems.
New Foundations for Information Theory by David Ellerman Pdf
This monograph offers a new foundation for information theory that is based on the notion of information-as-distinctions, being directly measured by logical entropy, and on the re-quantification as Shannon entropy, which is the fundamental concept for the theory of coding and communications. Information is based on distinctions, differences, distinguishability, and diversity. Information sets are defined that express the distinctions made by a partition, e.g., the inverse-image of a random variable so they represent the pre-probability notion of information. Then logical entropy is a probability measure on the information sets, the probability that on two independent trials, a distinction or “dit” of the partition will be obtained. The formula for logical entropy is a new derivation of an old formula that goes back to the early twentieth century and has been re-derived many times in different contexts. As a probability measure, all the compound notions of joint, conditional, and mutual logical entropy are immediate. The Shannon entropy (which is not defined as a measure in the sense of measure theory) and its compound notions are then derived from a non-linear dit-to-bit transform that re-quantifies the distinctions of a random variable in terms of bits—so the Shannon entropy is the average number of binary distinctions or bits necessary to make all the distinctions of the random variable. And, using a linearization method, all the set concepts in this logical information theory naturally extend to vector spaces in general—and to Hilbert spaces in particular—for quantum logical information theory which provides the natural measure of the distinctions made in quantum measurement. Relatively short but dense in content, this work can be a reference to researchers and graduate students doing investigations in information theory, maximum entropy methods in physics, engineering, and statistics, and to all those with a special interest in a new approach to quantum information theory.
Quantum Foundations, Probability and Information by Andrei Khrennikov,Bourama Toni Pdf
Composed of contributions from leading experts in quantum foundations, this volume presents viewpoints on a number of complex problems through informational, probabilistic, and mathematical perspectives and features novel mathematical models of quantum and subquantum phenomena. Rich with multi-disciplinary mathematical content, this book includes applications of partial differential equations in quantum field theory, differential geometry, oscillatory processes and vibrations, and Feynman integrals for quickly growing potential functions. Due to rapid growth in the field in recent years, this volume aims to promote interdisciplinary collaboration in the areas of quantum probability, information, communication and foundation, and mathematical physics. Many papers discuss complex yet novel problems that depart from the mainstream of quantum physical studies. Others devote explanation to fundamental problems of the conventional quantum theory, including its mathematical formalism. Overall, authors cover a diverse set of topics, including quantum and classical field theory and oscillatory processing, quantum mechanics from a Darwinian evolutionary perspective, and biological applications of quantum theory. Together in one volume, these essays will be useful to experts in the corresponding areas of quantum theory. Theoreticians, experimenters, mathematicians, and even philosophers in quantum physics and quantum probability and information theory can consider this book a valuable resource.
Modern Quantum Theory by Reinhold Bertlmann,Nicolai Friis Pdf
In the last few decades quantum theory has experienced an extensive revival owing to the rapid development of quantum information and quantum technologies. Based on a series of courses taught by the authors, the book takes the reader on a journey from the beginnings of quantum theory in the early twentieth century to the realm of quantum-information processing in the twenty-first. The central aim of this textbook, therefore, is to offer a detailed introduction to quantum theory that covers both physical and information-theoretic aspects, with a particular focus on the concept of entanglement and its characteristics, variants, and applications. Suitable for undergraduate students in physics and related subjects who encounter quantum mechanics for the first time, this book also serves as a resource for graduate students who want to engage with more advanced topics, offering a collection of derivations, proofs, technical methods, and references for graduate students and more experienced readers engaged with teaching and active research. The book is divided into three parts: Part I - Quantum Mechanics, Part II - Entanglement and Non-Locality, and Part III - Advanced Topics in Modern Quantum Physics. Part I provides a modern view on quantum mechanics, a central topic of theoretical physics. Part II is dedicated to the foundations of quantum mechanics and entanglement: starting with density operators, hidden-variable theories, the Einstein-Podolsky-Rosen Paradox, and Bell Inequalities, but also touching upon philosophical questions, followed by a deeper study of entanglement-based quantum communication protocols like teleportation, before giving a detailed exposition of entanglement theory, including tools for the detection and quantification of entanglement. Part III is intended as a collection of standalone chapters to supplement the contents of Parts I and II, covering more advanced topics such as classical and quantum entropies, quantum operations and measurements, decoherence, quantum metrology and quantum optics, and entanglement in particle physics.
The Statistical Foundations Of Entropy by John D Ramshaw Pdf
This book presents an innovative unified approach to the statistical foundations of entropy and the fundamentals of equilibrium statistical mechanics. These intimately related subjects are often developed in a fragmented historical manner which obscures the essential simplicity of their logical structure. In contrast, this book critically reassesses and systematically reorganizes the basic concepts into a simpler sequential framework which reveals more clearly their logical relationships. The inherent indistinguishability of identical particles is emphasized, and the resulting unification of classical and quantum statistics is discussed in detail.The discussion is focused entirely on fundamental concepts, so applications are omitted. The book is written at the advanced undergraduate or beginning graduate level, and will be useful as a concise supplement to conventional books and courses in statistical mechanics, thermal physics, and thermodynamics. It is also suitable for self-study by those seeking a deeper and more detailed analysis of the fundamentals.
Quantum Entropy and Its Use by M. Ohya,Denes Petz Pdf
Numerous fundamental properties of quantum information measurement are developed, including the von Neumann entropy of a statistical operator and its limiting normalized version, the entropy rate. Use of quantum-entropy quantities is made in perturbation theory, central limit theorems, thermodynamics of spin systems, entropic uncertainty relations, and optical communication. This new softcover corrected reprint contains summaries of recent developments added to the ends of the chapters.
What is Quantum Information? by Olimpia Lombardi,Sebastian Fortin,Federico Holik,Cristian López Pdf
Combining physics and philosophy, this is a uniquely interdisciplinary examination of quantum information science. Suitable as both a discussion of the conceptual and philosophical problems of this field and a comprehensive stand-alone introduction, this book will benefit both experienced and new researchers in quantum information and the philosophy of physics.
Complexity, Entropy And The Physics Of Information by Wojciech H. Zurek Pdf
This book has emerged from a meeting held during the week of May 29 to June 2, 1989, at St. John’s College in Santa Fe under the auspices of the Santa Fe Institute. The (approximately 40) official participants as well as equally numerous “groupies” were enticed to Santa Fe by the above “manifesto.” The book—like the “Complexity, Entropy and the Physics of Information” meeting explores not only the connections between quantum and classical physics, information and its transfer, computation, and their significance for the formulation of physical theories, but it also considers the origins and evolution of the information-processing entities, their complexity, and the manner in which they analyze their perceptions to form models of the Universe. As a result, the contributions can be divided into distinct sections only with some difficulty. Indeed, I regard this degree of overlapping as a measure of the success of the meeting. It signifies consensus about the important questions and on the anticipated answers: they presumably lie somewhere in the “border territory,” where information, physics, complexity, quantum, and computation all meet.
