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Temporal Quantum Correlations and Hidden Variable Models

Temporal Quantum Correlations and Hidden Variable Models
Author: Costantino Budroni
Publisher: Springer
Total Pages: 114
Release: 2015-10-22
Genre: Science
ISBN: 3319241699

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In this thesis, the main approach to the characterization of the set of classical probabilities, the correlation polytope approach, is reviewed for different scenarios, namely, hidden variable models discussed by Bell (local), Kochen and Specker (non-contextual), and Leggett and Garg (macrorealist). Computational difficulties associated with the method are described and a method to overcome them in several nontrivial cases is presented. For the quantum case, a general method to analyze quantum correlations in the sequential measurement scenario is provided, which allows computation of the maximal correlations. Such a method has a direct application for computation of maximal quantum violations of Leggett-Garg inequalities and it is relevant in the analysis of non-contextuality tests. Finally, possible applications of the results for quantum information tasks are discussed.


Probing the Structure of Quantum Mechanics

Probing the Structure of Quantum Mechanics
Author: Diederik Aerts
Publisher: World Scientific
Total Pages: 400
Release: 2002-06-11
Genre: Science
ISBN: 9814489409

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During the last decade, scientists working in quantum theory have been engaging in promising new fields such as quantum computation and quantum information processing, and have also been reflecting on the possibilities of nonlinear behavior on the quantum level. These are challenging undertakings because (1) they will result in new solutions to important technical and practical problems that were unsolvable by the classical approaches (for example, quantum computers can calculate problems that are intractable if one uses classical computers); and (2) they open up new 'hard' problems of a fundamental nature that touch the foundation of quantum theory itself (for example, the contradiction between locality and nonlinearity and the interpretation of quantum computing as a universal process). In this book, one can distinguish two main streams of research to approach the just-mentioned problem field: (1) a theoretical structural part, which concentrates on the elaboration of a nonlinear quantum mechanics and the fundamentals of quantum computation; and (2) a theoretical experimental part, which focuses on the theoretical aspects of applications that arise from new technology and novel research perspectives such as quantum optics and quantum cryptography. Particular attention is also paid to the measurement problem, the classical limit and alternative interpretations (such as the hidden measurement approach). Contents:Probing the Structure of Quantum Mechanics (D Aerts et al.)The Linearity of Quantum Mechanics at Stake: The Description of Separated Quantum Entities (D Aerts & F Valckenborgh)Linearity and Compound Physical Systems: The Case of Two Separated Spin 1/2 Entities (D Aerts & F Valckenborgh)Being and Change: Foundations of a Realistic Operational Formalism (D Aerts)The Classical Limit of the Lattice-Theoretical Orthocomplementation in the Framework of the Hidden-Measurement Approach (T Durt & B D'Hooghe)State Property Systems and Closure Spaces: Extracting the Classical en Non-Classical Parts (D Aerts & D Deses)Hidden Measurements from Contextual Axiomatics (S Aerts)High Energy Approaches to Low Energy Phenomena in Astrophysics (S M Austin)Memory Effects in Atomic Interferometry: A Negative Result (T Durt et al.)Reality and Probability: Introducing a New Type of Probability Calculus (D Aerts)Quantum Computation: Towards the Construction of a ‘Between Quantum and Classical Computer’ (D Aerts & B D'Hooghe)Buckley-Siler Connectives for Quantum Logics of Fuzzy Sets (J Pykacz & B D'Hooghe)Some Notes on Aerts' Interpretation of the EPR-Paradox and the Violation of Bell-Inequalities (W Christiaens)Quantum Cryptographic Encryption in Three Complementary Bases Through a Mach-Zehnder Set Up (T Durt & B Nagler)Quantum Cryptography Without Quantum Uncertainties (T Durt)How to Construct Darboux-Invariant Equations of von Neumann Type (J L Cie(li(ski)Darboux-Integrable Equations with Non-Abelian Nonlinearities (N V Ustinov & M Czachor)Dressing Chain Equations Associated with Difference Soliton Systems (S Leble)Covariance Approach to the Free Photon Field (M Kuna & J Naudts) Readership: Graduate students, researchers and academics in quantum physics. Keywords:Quantum Mechanics;Quantum Computation;Quantum Information Processing


Lectures on General Quantum Correlations and their Applications

Lectures on General Quantum Correlations and their Applications
Author: Felipe Fernandes Fanchini
Publisher: Springer
Total Pages: 534
Release: 2017-06-24
Genre: Science
ISBN: 3319534122

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This book presents a distinctive way of understanding quantum correlations beyond entanglement, introducing readers to this less explored yet very fundamental aspect of quantum theory. It takes into account most of the new ideas involving quantum phenomena, resources, and applications without entanglement, both from a theoretical and an experimental point of view. This book serves as a reference for both beginner students and experienced researchers in physics and applied mathematics, with an interest in joining this novel venture towards understanding the quantum nature of the world.


Quantum Correlations in Field Theory and Integrable Systems

Quantum Correlations in Field Theory and Integrable Systems
Author: Stefano Evangelisti
Publisher: Minkowski Institute Press
Total Pages: 213
Release: 2013-05-31
Genre: Science
ISBN: 1927763096

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This doctoral thesis analytically and numerically examines some of the most important concepts in quantum correlations in low-dimensional physics: entanglement and out-of-equilibrium dynamics. As John Bell once said: "Entanglement expresses the spooky nonlocality inherent to quantum mechanics", and its study not only concerns the foundations of any quantum theory, but also has important applications in quantum information and condensed matter theory, amongst others. The first chapters are devoted to the study of "entanglement entropies", a popular measure of the "quantumness" of a physical system. The main focus of the analysis is the one-dimensional XYZ spin-1/2 chain in equilibrium, an interacting theory which in addition to being integrable also has interesting scaling limits, such as the sine-Gordon field theory. Moving away from equilibrium the subsequent chapters deal with the dynamics of quantum correlators after an instantaneous quantum quench. The emphasis is on two different models and techniques; the transverse field Ising chain is studied using the form-factor approach and the O(3) non-linear sigma model is studied by means of the semi-classical theory. In the final chapter the author highlights an important general result: in the absence of long-range interactions in the final Hamiltonian the dynamics of a quantum system are determined by the same statistical ensemble that describes static correlations.


Non-locality and Modality

Non-locality and Modality
Author: Tomasz Placek
Publisher: Springer Science & Business Media
Total Pages: 345
Release: 2012-12-06
Genre: Science
ISBN: 9401003858

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Quantum theory is the most successful of all physical theories: it has a towering mathematical structure, a vast range of accurate predictions, and technological applications. Its interpretation, however, is as unsettled now as in the heroic days of Einstein and Bohr. This book focuses on quantum non-locality, the curious quantum correlations between spatially separated systems. Quantum non-locality was one subject of the debates between Einstein, Bohr and others such as Schrödinger. The topic was revived in the 1960s as a result of Bell's epoch-making theorems; since then it has been a very active research field, both theoretically and experimentally. This book contains twenty new papers by eminent researchers, who report recent developments in both the physics of the subject and its philosophy. The physics topics covered include quantum information, the unsharp (positive-operator) approach to observables, the state-space approach, and the pilot-wave theory. The philosophy papers include precise studies of Bohr's reply to the original Einstein-Podolsky-Rosen non-locality paradox, and of non-locality's relation to causation, probability and modality.


Measurements in Quantum Mechanics

Measurements in Quantum Mechanics
Author: Mohammad Reza Pahlavani
Publisher: BoD – Books on Demand
Total Pages: 363
Release: 2012-02-22
Genre: Science
ISBN: 9535100580

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Perhaps quantum mechanics is viewed as the most remarkable development in 20th century physics. Each successful theory is exclusively concerned about "results of measurement". Quantum mechanics point of view is completely different from classical physics in measurement, because in microscopic world of quantum mechanics, a direct measurement as classical form is impossible. Therefore, over the years of developments of quantum mechanics, always challenging part of quantum mechanics lies in measurements. This book has been written by an international invited group of authors and it is created to clarify different interpretation about measurement in quantum mechanics.


Bananaworld

Bananaworld
Author: Jeffrey Bub
Publisher: Oxford University Press
Total Pages: 289
Release: 2016
Genre: Science
ISBN: 0198718535

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What on earth do bananas have to do with quantum mechanics? From a modern perspective, quantum mechanics is about strangely counterintuitive correlations between separated systems, which can be exploited in feats like quantum teleportation, unbreakable cryptographic schemes, and computers with enormously enhanced computing power. Schro'dinger coined the term "entanglement" to describe these bizarre correlations. Bananaworld -- an imaginary island with "entangled" bananas -- brings to life the fascinating discoveries of the new field of quantum information without the mathematical machinery of quantum mechanics. The connection with quantum correlations is fully explained in sections written for the non-physicist reader with a serious interest in understanding the mysteries of the quantum world. The result is a subversive but entertaining book that is accessible and interesting to a wide range of readers, with the novel thesis that quantum mechanics is about the structure of information. What we have discovered is that the possibilities for representing, manipulating, and communicating information are very different than we thought.


Probabilities, Causes and Propensities in Physics

Probabilities, Causes and Propensities in Physics
Author: Mauricio Suárez
Publisher: Springer Science & Business Media
Total Pages: 259
Release: 2010-12-06
Genre: Science
ISBN: 1402099045

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This volume defends a novel approach to the philosophy of physics: it is the first book devoted to a comparative study of probability, causality, and propensity, and their various interrelations, within the context of contemporary physics -- particularly quantum and statistical physics. The philosophical debates and distinctions are firmly grounded upon examples from actual physics, thus exemplifying a robustly empiricist approach. The essays, by both prominent scholars in the field and promising young researchers, constitute a pioneer effort in bringing out the connections between probabilistic, causal and dispositional aspects of the quantum domain. The book will appeal to specialists in philosophy and foundations of physics, philosophy of science in general, metaphysics, ontology of physics theories, and philosophy of probability.


Fractals of Brain, Fractals of Mind

Fractals of Brain, Fractals of Mind
Author: Earl Mac Cormac
Publisher: John Benjamins Publishing
Total Pages: 371
Release: 1996-06-28
Genre: Psychology
ISBN: 902728489X

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This collective volume is the first to discuss systematically what are the possibilities to model different aspects of brain and mind functioning with the formal means of fractal geometry and deterministic chaos. At stake here is not an approximation to the way of actual performance, but the possibility of brain and mind to implement nonlinear dynamic patterns in their functioning. The contributions discuss the following topics (among others): the edge-of-chaos dynamics in recursively organized neural systems and in intersensory interaction, the fractal timing of the neural functioning on different scales of brain networking, aspects of fractal neurodynamics and quantum chaos in novel biophysics, the fractal maximum-power evolution of brain and mind, the chaotic dynamics in the development of consciousness, etc. It is suggested that the ‘margins’ of our capacity for phenomenal experience, are ‘fractal-limit phenomena’. Here the possibilities to prove the plausibility of fractal modeling with appropriate experimentation and rational reconstruction are also discussed. A conjecture is made that the brain vs. mind differentiation becomes possible, most probably, only with the imposition of appropriate symmetry groups implementing a flowing interface of features of local vs. global brain dynamics. (Series B)