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Entanglement Measures And Their Properties In Quantum Field Theory
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Book Synopsis Entanglement Measures and Their Properties in Quantum Field Theory by : Stefan Hollands
Download or read book Entanglement Measures and Their Properties in Quantum Field Theory written by Stefan Hollands and published by Springer. This book was released on 2018-10-12 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a rigorous treatment of entanglement measures in the general context of quantum field theory. It covers a broad range of models and the use of fields allows us to properly take the localization of systems into account. The required mathematical techniques are introduced in a self-contained way.
Book Synopsis Progress and Visions in Quantum Theory in View of Gravity by : Felix Finster
Download or read book Progress and Visions in Quantum Theory in View of Gravity written by Felix Finster and published by Springer Nature. This book was released on 2020-04-09 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on a critical discussion of the status and prospects of current approaches in quantum mechanics and quantum field theory, in particular concerning gravity. It contains a carefully selected cross-section of lectures and discussions at the seventh conference “Progress and Visions in Quantum Theory in View of Gravity” which took place in fall 2018 at the Max Planck Institute for Mathematics in the Sciences in Leipzig. In contrast to usual proceeding volumes, instead of reporting on the most recent technical results, contributors were asked to discuss visions and new ideas in foundational physics, in particular concerning foundations of quantum field theory. A special focus has been put on the question of which physical principles of quantum (field) theory can be considered fundamental in view of gravity. The book is mainly addressed to mathematicians and physicists who are interested in fundamental questions of mathematical physics. It allows the reader to obtain a broad and up-to-date overview of a fascinating active research area.
Book Synopsis Frontiers in Quantum Information Research by : Mikio Nakahara
Download or read book Frontiers in Quantum Information Research written by Mikio Nakahara and published by World Scientific. This book was released on 2012 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Counting Degrees of Freedom in Quantum Field Theory Using Entanglement Entropy by : Márk Koppany Mezei
Download or read book Counting Degrees of Freedom in Quantum Field Theory Using Entanglement Entropy written by Márk Koppany Mezei and published by . This book was released on 2014 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: We devote this thesis to the exploration of how to define the number of degrees of freedom in quantum field theory. Intuitively, the number of degrees of freedom should decrease along the renormalization group (RG) flow, and should be independent of the RG scale at a conformal fixed point. We argue that a refinement of entanglement entropy is a promising candidate for such measure. Indeed, in two and three spacetime dimensions the number of degrees of freedom defined this way can be proven to monotonically decrease under RG flows. Firstly, we define renormalized entanglement entropy (REE) and show that it is finite in the continuum limit in a renormalizable field theory. We argue that it is most sensitive to degrees of freedom at a scale determined by the size of the entangling region, and interpolates between the ultraviolet and infrared RG fixed point vales. We discuss how it can be used to count the degrees of freedom at a given scale. Secondly, we test whether REE is monotonic along the RG flow. In two dimensions it was known to be monotonic before our study. In higher dimensions, we study REE in free theory examples and in the framework of holography. Holography is tailormade for the study of RG flows, and allows an efficient determination of entanglement entropy. We make use of its power and flexibility to conjecture that in three spacetime dimensions REE is monotonic, while in four dimensions it is neither monotonic nor positive. Subsequent work has proven the conjecture. Thirdly, we count the degrees of freedom in three-dimensional superconformal field theories that are the infrared limit of supersymrnetric gauge theories with matter. Supersymmetric localization reduces the computation of entanglement entropy to a matrix integral. We solve this matrix model in the large N number of colors limit using two different methods; in a saddle point approximation we obtain the next-to-leading order expression in 1/N, while mapping the matrix model to a non-interacting Fermi gas enables us to determine the result to all orders in 1/N. We match the leading piece with N3/ 2 scaling - a strong coupling phenomenon in the field theory - with the holographic duals of these theories. Establishing a measure for the number of degrees of freedom provides nonperturbative understanding of RG fixed points and flows. Our hope is that the constraints coming from RG monotonicity can be efficiently used to constrain the long-distance physics of certain systems of interest. The first applications are only starting to emerge.
Author :Hannu Christian Wichterich Publisher :Springer Science & Business Media ISBN 13 :3642193420 Total Pages :121 pages Book Rating :4.6/5 (421 download)
Book Synopsis Entanglement Between Noncomplementary Parts of Many-Body Systems by : Hannu Christian Wichterich
Download or read book Entanglement Between Noncomplementary Parts of Many-Body Systems written by Hannu Christian Wichterich and published by Springer Science & Business Media. This book was released on 2011-05-18 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis investigates the structure and behaviour of entanglement, the purely quantum mechanical part of correlations, in many-body systems, employing both numerical and analytical techniques at the interface of condensed matter theory and quantum information theory. Entanglement can be seen as a precious resource which, for example, enables the noiseless and instant transmission of quantum information, provided the communicating parties share a sufficient "amount" of it. Furthermore, measures of entanglement of a quantum mechanical state are perceived as useful probes of collective properties of many-body systems. For instance, certain measures are capable of detecting and classifying ground-state phases and, particularly, transition (or critical) points separating such phases. Chapters 2 and 3 focus on entanglement in many-body systems and its use as a potential resource for communication protocols. They address the questions of how a substantial amount of entanglement can be established between distant subsystems, and how efficiently this entanglement could be "harvested" by way of measurements. The subsequent chapters 4 and 5 are devoted to universality of entanglement between large collections of particles undergoing a quantum phase transition, where, despite the enormous complexity of these systems, collective properties including entanglement no longer depend crucially on the microscopic details.
Book Synopsis Entanglement measures in quantum field theory by : Sofía Garzón Mora
Download or read book Entanglement measures in quantum field theory written by Sofía Garzón Mora and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "El enredamiento surge en sistemas a partir de correlaciones cuánticas sin contraparte clásica. Por lo tanto, introducimos medidas de enredamiento en el contexto de sistemas cuánticos bipartitos como una forma de cuantificarlas. Para estados puros obtenemos que la única medida de enredamiento es la entropía de von Neumann, que puede expresarse en términos de pares de Bell. Sin embargo, para estados mixtos esta unicidad se pierde. Por esto, mencionamos algunas medidas de enredamiento usando teoría modular de operadores para el caso de estados mixtos en sistemas con infinitos grados de libertad, principalmente empleando la Teoría Cuántica de Campos, y probamos algunas de sus propiedades. Adicionalmente, caracterizamos canales cuánticos en términos de mapas completamente positivos y obtenemos un tipo de operaciones realizadas en un sistema que no aumentan su enredamiento." -- Tomado del Formato de Documento de Grado.
Book Synopsis Quantum Entanglement in High Energy Physics by : Oliver K. Baker
Download or read book Quantum Entanglement in High Energy Physics written by Oliver K. Baker and published by BoD – Books on Demand. This book was released on 2024-04-24 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to research topics in quantum entanglement at the energy frontier of particle and nuclear physics, and important interdisciplinary collaborations with colleagues from fields outside of physics. A non-exhaustive list of examples of the latter can include mathematics, computer science, social sciences, philosophy, and how physics can interact with them in a way that supports successful outcomes. These are exciting times in the field of quantum information science, with new research results and their applications in society exhibiting themselves rather frequently. But what is even more exciting is that the frequency of these new results and their applications increases with a rapidity that will motivate new methods, new theories, new experiments, and new collaborations outside of the field that future researchers will find quite challenging.
Book Synopsis Quantum Correlations in Field Theory and Integrable Systems by : Stefano Evangelisti
Download or read book Quantum Correlations in Field Theory and Integrable Systems written by Stefano Evangelisti and published by Minkowski Institute Press. This book was released on 2013-05-31 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quantum Entanglement for Babies by : Chris Ferrie
Download or read book Quantum Entanglement for Babies written by Chris Ferrie and published by Sourcebooks, Inc.. This book was released on 2017-07-04 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finally, a scientific series that treats babies like the geniuses they are! With scientific and mathematical information from an expert, this is the perfect book for the next Einstein. Written by an expert, Quantum Entanglement for Babies is a colorfully simple introduction to one of nature's weirdest phenomenons. Babies (and grownups!) will learn about the wild world of quantum particles. With a tongue-in-cheek approach that adults will love, this installment of the Baby University board book series is the perfect way to introduce basic concepts to even the youngest scientists. After all, it's never too early to become a quantum physicist! Baby University: It only takes a small spark to ignite a child's mind.
Book Synopsis Topology and Quantum Theory in Interaction by : David Ayala
Download or read book Topology and Quantum Theory in Interaction written by David Ayala and published by American Mathematical Soc.. This book was released on 2018-10-25 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the NSF-CBMS Regional Conference on Topological and Geometric Methods in QFT, held from July 31–August 4, 2017, at Montana State University in Bozeman, Montana. In recent decades, there has been a movement to axiomatize quantum field theory into a mathematical structure. In a different direction, one can ask to test these axiom systems against physics. Can they be used to rederive known facts about quantum theories or, better yet, be the framework in which to solve open problems? Recently, Freed and Hopkins have provided a solution to a classification problem in condensed matter theory, which is ultimately based on the field theory axioms of Graeme Segal. Papers contained in this volume amplify various aspects of the Freed–Hopkins program, develop some category theory, which lies behind the cobordism hypothesis, the major structure theorem for topological field theories, and relate to Costello's approach to perturbative quantum field theory. Two papers on the latter use this framework to recover fundamental results about some physical theories: two-dimensional sigma-models and the bosonic string. Perhaps it is surprising that such sparse axiom systems encode enough structure to prove important results in physics. These successes can be taken as encouragement that the axiom systems are at least on the right track toward articulating what a quantum field theory is.
Download or read book Quantum Entanglement written by Jed Brody and published by MIT Press. This book was released on 2020-02-18 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: An exploration of quantum entanglement and the ways in which it contradicts our everyday assumptions about the ultimate nature of reality. Quantum physics is notable for its brazen defiance of common sense. (Think of Schrödinger's Cat, famously both dead and alive.) An especially rigorous form of quantum contradiction occurs in experiments with entangled particles. Our common assumption is that objects have properties whether or not anyone is observing them, and the measurement of one can't affect the other. Quantum entanglement—called by Einstein “spooky action at a distance”—rejects this assumption, offering impeccable reasoning and irrefutable evidence of the opposite. Is quantum entanglement mystical, or just mystifying? In this volume in the MIT Press Essential Knowledge series, Jed Brody equips readers to decide for themselves. He explains how our commonsense assumptions impose constraints—from which entangled particles break free. Brody explores such concepts as local realism, Bell's inequality, polarization, time dilation, and special relativity. He introduces readers to imaginary physicists Alice and Bob and their photon analyses; points out that it's easier to reject falsehood than establish the truth; and reports that some physicists explain entanglement by arguing that we live in a cross-section of a higher-dimensional reality. He examines a variety of viewpoints held by physicists, including quantum decoherence, Niels Bohr's Copenhagen interpretation, genuine fortuitousness, and QBism. This relatively recent interpretation, an abbreviation of “quantum Bayesianism,” holds that there's no such thing as an absolutely accurate, objective probability “out there,” that quantum mechanical probabilities are subjective judgments, and there's no “action at a distance,” spooky or otherwise.
Book Synopsis Geometry of Quantum States by : Ingemar Bengtsson
Download or read book Geometry of Quantum States written by Ingemar Bengtsson and published by Cambridge University Press. This book was released on 2017-08-18 with total page 637 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Universal Coefficient Theorem and Quantum Field Theory by : Andrei-Tudor Patrascu
Download or read book The Universal Coefficient Theorem and Quantum Field Theory written by Andrei-Tudor Patrascu and published by Springer. This book was released on 2016-09-23 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis describes a new connection between algebraic geometry, topology, number theory and quantum field theory. It offers a pedagogical introduction to algebraic topology, allowing readers to rapidly develop basic skills, and it also presents original ideas to inspire new research in the quest for dualities. Its ambitious goal is to construct a method based on the universal coefficient theorem for identifying new dualities connecting different domains of quantum field theory. This thesis opens a new area of research in the domain of non-perturbative physics—one in which the use of different coefficient structures in (co)homology may lead to previously unknown connections between different regimes of quantum field theories. The origin of dualities is an issue in fundamental physics that continues to puzzle the research community with unexpected results like the AdS/CFT duality or the ER-EPR conjecture. This thesis analyzes these observations from a novel and original point of view, mainly based on a fundamental connection between number theory and topology. Beyond its scientific qualities, it also offers a pedagogical introduction to advanced mathematics and its connection with physics. This makes it a valuable resource for students in mathematical physics and researchers wanting to gain insights into (co)homology theories with coefficients or the way in which Grothendieck's work may be connected with physics.
Book Synopsis Lectures on General Quantum Correlations and their Applications by : Felipe Fernandes Fanchini
Download or read book Lectures on General Quantum Correlations and their Applications written by Felipe Fernandes Fanchini and published by Springer. This book was released on 2017-06-24 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Strongly Coupled Field Theories for Condensed Matter and Quantum Information Theory by : Alvaro Ferraz
Download or read book Strongly Coupled Field Theories for Condensed Matter and Quantum Information Theory written by Alvaro Ferraz and published by Springer Nature. This book was released on 2020-02-29 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a selection of advanced lectures from leading researchers, providing recent theoretical results on strongly coupled quantum field theories. It also analyzes their use for describing new quantum states, which are physically realizable in condensed matter, cold-atomic systems, as well as artificial materials. It particularly focuses on the engineering of these states in quantum devices and novel materials useful for quantum information processing. The book offers graduate students and young researchers in the field of modern condensed matter theory an updated review of the most relevant theoretical methods used in strongly coupled field theory and string theory. It also provides the tools for understanding their relevance in describing the emergence of new quantum states in a variety of physical settings. Specifically, this proceedings book summarizes new and previously unrelated developments in modern condensed matter physics, in particular: the interface of condensed matter theory and quantum information theory; the interface of condensed matter physics and the mathematics emerging from the classification of the topological phases of matter, such as topological insulators and topological superconductors; and the simulation of condensed matter systems with cold atoms in optical lattices.
Book Synopsis Measurements in Quantum Mechanics by : Mohammad Reza Pahlavani
Download or read book Measurements in Quantum Mechanics written by Mohammad Reza Pahlavani and published by BoD – Books on Demand. This book was released on 2012-02-22 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quantum Information Theory by : Mark Wilde
Download or read book Quantum Information Theory written by Mark Wilde and published by Cambridge University Press. This book was released on 2013-04-18 with total page 673 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained, graduate-level textbook that develops from scratch classical results as well as advances of the past decade.
