Download or read book Quantum Foundations Probability and Information written by Andrei Khrennikov and published by Springer. This book was released on 2018-06-13 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Quantum Information Theory and the Foundations of Quantum Mechanics written by Christopher G. Timpson and published by Oxford Philosophical Monograph. This book was released on 2013-04-25 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Christopher G. Timpson provides the first full-length philosophical treatment of quantum information theory and the questions it raises for our understanding of the quantum world. He argues for an ontologically deflationary account of the nature of quantum information, which is grounded in a revisionary analysis of the concepts of information.
Download or read book Quantum Information Theory and Quantum Statistics written by Dénes Petz and published by Springer Science & Business Media. This book was released on 2007-10-20 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise and readable book addresses primarily readers with a background in classical statistical physics and introduces quantum mechanical notions as required. Conceived as a primer to bridge the gap between statistical physics and quantum information, it emphasizes concepts and thorough discussions of the fundamental notions and prepares the reader for deeper studies, not least through a selection of well chosen exercises.
Download or read book Quantum Theory Informational Foundations and Foils written by Giulio Chiribella and published by Springer. This book was released on 2015-12-08 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the first unified overview of the burgeoning research area at the interface between Quantum Foundations and Quantum Information. Topics include: operational alternatives to quantum theory, information-theoretic reconstructions of the quantum formalism, mathematical frameworks for operational theories, and device-independent features of the set of quantum correlations. Powered by the injection of fresh ideas from the field of Quantum Information and Computation, the foundations of Quantum Mechanics are in the midst of a renaissance. The last two decades have seen an explosion of new results and research directions, attracting broad interest in the scientific community. The variety and number of different approaches, however, makes it challenging for a newcomer to obtain a big picture of the field and of its high-level goals. Here, fourteen original contributions from leading experts in the field cover some of the most promising research directions that have emerged in the new wave of quantum foundations. The book is directed at researchers in physics, computer science, and mathematics and would be appropriate as the basis of a graduate course in Quantum Foundations.
Download or read book Probability and Randomness written by Andre? I?U?r?evich Khrennikov and published by World Scientific. This book was released on 2016 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Creating a rigorous mathematical theory of randomness is far from being complete, even in the classical case. Interrelation of Classical and Quantum Randomness rectifies this and introduces mathematical formalisms of classical and quantum probability and randomness with brief discussion of their interrelation and interpretational and foundational issues. The book presents the essentials of classical approaches to randomness, enlightens their successes and problems, and then proceeds to essentials of quantum randomness. Its wide-ranging and comprehensive scope makes it suitable for researchers in mathematical physics, probability and statistics at any level"--
Download or read book Mathematical Foundations of Quantum Information and Computation and Its Applications to Nano and Bio systems written by Masanori Ohya and published by Springer Science & Business Media. This book was released on 2011-01-15 with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a mathematical foundation to the theory of quantum information and computation, with applications to various open systems including nano and bio systems. It includes introductory material on algorithm, functional analysis, probability theory, information theory, quantum mechanics and quantum field theory. Apart from standard material on quantum information like quantum algorithm and teleportation, the authors discuss findings on the theory of entropy in C*-dynamical systems, space-time dependence of quantum entangled states, entangling operators, adaptive dynamics, relativistic quantum information, and a new paradigm for quantum computation beyond the usual quantum Turing machine. Also, some important applications of information theory to genetics and life sciences, as well as recent experimental and theoretical discoveries in quantum photosynthesis are described.
Download or read book Quantum Foundations written by Pedro W. Lamberti and published by MDPI. This book was released on 2019-04-02 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Foundations of Probability and Physics 6 written by Mauro D'Ariano and published by American Institute of Physics. This book was released on 2012-04-26 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the 12th conference in Växjö, Sweden, which is devoted to quantum foundations and quantum information, especially the clarification of fundamental questions. The Växjö series is the longest continuous series of conferences devoted to quantum foundations in the history of quantum mechanics. During this conference, FPP6, we were fortunate to have not only physicists (theorists as well as experimentalists), but also mathematicians and several philosophers discussing the foundations of quantum theory, especially in the light of recent developments of quantum information theory. Fundamental questions of quantum mechanics, especially information theory, quantum computing, cryptography and teleportation have continued to be central topics in this series of conferences.
Download or read book Foundations of Probability and Physics 5 written by Luigi Accardi and published by American Institute of Physics. This book was released on 2009-04-03 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This conference was devoted to fundamental questions raised by quantum mechanics, especially in quantum information theory. As has become customary in our series of conference in Växjö, we were glad to welcome a fruitful assembly of theoretical physicists, experimentalists, mathematicians and even philosophers interested in the foundations of probability and physics. This conference belongs to the series of Växjö conferences in foundations of quantum mechanics (especially probabilistic foundations) combined of two subseries, Foundations of Probability and Physics: 2000, 02, 04, 06, 08, and Quantum Theory: Reconsideration of Foundations: 2001, 03, 05, 07. We also mention the first Växjö conference: Bohmian mechanics 2000. This is definitely the longest series of conferences on foundations in the history of quantum mechanics.
Download or read book Quantum Information and Foundations written by Giacomo Mauro D’Ariano and published by MDPI. This book was released on 2020-03-23 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Foundations of Probability and Physics 3 written by Andrei Khrennikov and published by American Inst. of Physics. This book was released on 2005-03-03 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This conference is one of a series of Växjö conferences on the foundations of quantummechanics. The main aim of this conference was to understand the role that probability plays in the foundations of physics, theoretical as well as experimental. It should be emphasized that nowadays the problems of probabilistic foundations are not of purely theoretical interest. These problems play a fundamental role in future development of quantum computing and cryptography. At this conference we were fortunate to have a mixture of outstanding physicists, mathematicians, and even philosophers interested in scientific foundations in attendance. The following problems were discussed: unification of classical and quantum probability theories, EPR-Bohm and theoriginal EPR experiments, Bell's inequality: interpretations of its violation and loopholes,simulation of EPR-Bohm correlations in the local realistic approach, nonlocality, contextual probabilistic models, subjective probability and quantum information, quantum logic, results of recent experiments in quantum information, philosophic foundations of probability and quantum mechanics, model theory, discrete time and dynamics.
Download or read book New Foundations for Information Theory written by David Ellerman and published by Springer Nature. This book was released on 2021-10-30 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Probabilistic and Statistical Aspects of Quantum Theory written by Alexander S. Holevo and published by Springer Science & Business Media. This book was released on 2011-05-05 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to aspects of the foundations of quantum mechanics in which probabilistic and statistical concepts play an essential role. The main part of the book concerns the quantitative statistical theory of quantum measurement, based on the notion of positive operator-valued measures. During the past years there has been substantial progress in this direction, stimulated to a great extent by new applications such as Quantum Optics, Quantum Communication and high-precision experiments. The questions of statistical interpretation, quantum symmetries, theory of canonical commutation relations and Gaussian states, uncertainty relations as well as new fundamental bounds concerning the accuracy of quantum measurements, are discussed in this book in an accessible yet rigorous way. Compared to the first edition, there is a new Supplement devoted to the hidden variable issue. Comments and the bibliography have also been extended and updated.
Download or read book Proceedings of the Conference Foundations of Probability and Physics written by A. Khrennikov and published by World Scientific. This book was released on 2001 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, leading experts in experimental as well as theoretical physics (both classical and quantum) and probability theory give their views on many intriguing (and still mysterious) problems regarding the probabilistic foundations of physics. The problems discussed during the conference include EinsteinOCoPodolskyOCoRosen paradox, Bell's inequality, realism, nonlocality, role of Kolmogorov model of probability theory in quantum physics, von Mises frequency theory, quantum information, computation, OC quantum effectsOCO in classical physics. Contents: Locality and Bell's Inequality (L Accardi & M Regoli); Refutation of Bell's Theorem (G Adenier); Forcing Discretization and Determination in Quantum History Theories (B Coecke); Some Remarks on Hardy Functions Associated with Dirichlet Series (W Ehm); Ensemble Probabilistic Equilibrium and Non-Equilibrium Thermodynamics without the Thermodynamic Limit (D H E Gross); An Approach to Quantum Probability (S Gudder); Innovation Approach to Stochastic Processes and Quantum Dynamics (T Hida); Origin of Quantum Probabilities (A Khrennikov); OC ComplementarityOCO or Schizophrenia: Is Probability in Quantum Mechanics Information or Onta? (A F Kracklauer); A Probabilistic Inequality for the KochenOCoSpecker Paradox (J-A Larsson); Quantum Stochastics. The New Approach to the Description of Quantum Measurements (E Loubenets); Is Random Event a Core Question? Some Remarks and a Proposal (P Rocchi); Quantum Cryptography in Space and Bell's Theorem (I Volovich); and other papers. Readership: Graduate students and researchers in quantum physics, mathematical physics, theoretical physics, stochastic processes, and probability & statistics."
Download or read book Ubiquitous Quantum Structure written by Andrei Y. Khrennikov and published by Springer Science & Business Media. This book was released on 2010-01-23 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum-like structure is present practically everywhere. Quantum-like (QL) models, i.e. models based on the mathematical formalism of quantum mechanics and its generalizations can be successfully applied to cognitive science, psychology, genetics, economics, finances, and game theory. This book is not about quantum mechanics as a physical theory. The short review of quantum postulates is therefore mainly of historical value: quantum mechanics is just the first example of the successful application of non-Kolmogorov probabilities, the first step towards a contextual probabilistic description of natural, biological, psychological, social, economical or financial phenomena. A general contextual probabilistic model (Växjö model) is presented. It can be used for describing probabilities in both quantum and classical (statistical) mechanics as well as in the above mentioned phenomena. This model can be represented in a quantum-like way, namely, in complex and more general Hilbert spaces. In this way quantum probability is totally demystified: Born's representation of quantum probabilities by complex probability amplitudes, wave functions, is simply a special representation of this type.
Download or read book Foundations of Quantum Mechanics written by Emily Adlam and published by Cambridge University Press. This book was released on 2021-02-18 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics is an extraordinarily successful scientific theory. But more than 100 years after it was first introduced, the interpretation of the theory remains controversial. This Element introduces some of the most puzzling questions at the foundations of quantum mechanics and provides an up-to-date and forward-looking survey of the most prominent ways in which physicists and philosophers of physics have attempted to resolve them. Topics covered include nonlocality, contextuality, the reality of the wavefunction and the measurement problem. The discussion is supplemented with descriptions of some of the most important mathematical results from recent work in quantum foundations, including Bell's theorem, the Kochen-Specker theorem and the PBR theorem.
Download or read book Quantum Probability Quantum Logic written by Itamar Pitowsky and published by . This book was released on 2014-01-15 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
