Geometry of Quantum States

An Introduction to Quantum Entanglement

Author: Ingemar Bengtsson,Karol Życzkowski

Publisher: Cambridge University Press

ISBN: 1108293492

Category: Science

Page: N.A

View: 2624

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.
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Entanglement, Information, and the Interpretation of Quantum Mechanics

Author: Gregg Jaeger

Publisher: Springer Science & Business Media

ISBN: 3540921281

Category: Science

Page: 307

View: 3111

Entanglement was initially thought by some to be an oddity restricted to the realm of thought experiments. However, Bell’s inequality delimiting local - havior and the experimental demonstration of its violation more than 25 years ago made it entirely clear that non-local properties of pure quantum states are more than an intellectual curiosity. Entanglement and non-locality are now understood to ?gure prominently in the microphysical world, a realm into which technology is rapidly hurtling. Information theory is also increasingly recognized by physicists and philosophers as intimately related to the foun- tions of mechanics. The clearest indicator of this relationship is that between quantum information and entanglement. To some degree, a deep relationship between information and mechanics in the quantum context was already there to be seen upon the introduction by Max Born and Wolfgang Pauli of the idea that the essence of pure quantum states lies in their provision of probabilities regarding the behavior of quantum systems, via what has come to be known as the Born rule. The signi?cance of the relationship between mechanics and information became even clearer with Leo Szilard’s analysis of James Clerk Maxwell’s infamous demon thought experiment. Here, in addition to examining both entanglement and quantum infor- tion and their relationship, I endeavor to critically assess the in?uence of the study of these subjects on the interpretation of quantum theory.
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Topology and Geometry for Physics

Author: Helmut Eschrig

Publisher: Springer

ISBN: 3642147003

Category: Science

Page: 390

View: 3687

A concise but self-contained introduction of the central concepts of modern topology and differential geometry on a mathematical level is given specifically with applications in physics in mind. All basic concepts are systematically provided including sketches of the proofs of most statements. Smooth finite-dimensional manifolds, tensor and exterior calculus operating on them, homotopy, (co)homology theory including Morse theory of critical points, as well as the theory of fiber bundles and Riemannian geometry, are treated. Examples from physics comprise topological charges, the topology of periodic boundary conditions for solids, gauge fields, geometric phases in quantum physics and gravitation.
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Geometry of Quantum States, An Introduction to Quantum Entanglement

Physics, Quantum mechanics

Author: CTI Reviews

Publisher: Cram101 Textbook Reviews

ISBN: 1467204412

Category: Education

Page: 17

View: 9651

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.
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Local Quantum Physics

Fields, Particles, Algebras

Author: Rudolf Haag

Publisher: Springer Science & Business Media

ISBN: 3642614582

Category: Science

Page: 392

View: 7923

The new edition provided the opportunity of adding a new chapter entitled "Principles and Lessons of Quantum Physics". It was a tempting challenge to try to sharpen the points at issue in the long lasting debate on the Copenhagen Spirit, to assess the significance of various arguments from our present vantage point, seventy years after the advent of quantum theory, where, after ali, some problems appear in a different light. It includes a section on the assumptions leading to the specific mathematical formalism of quantum theory and a section entitled "The evolutionary picture" describing my personal conclusions. Alto gether the discussion suggests that the conventional language is too narrow and that neither the mathematical nor the conceptual structure are built for eter nity. Future theories will demand radical changes though not in the direction of a return to determinism. Essential lessons taught by Bohr will persist. This chapter is essentially self-contained. Some new material has been added in the last chapter. It concerns the char acterization of specific theories within the general frame and recent progress in quantum field theory on curved space-time manifolds. A few pages on renor malization have been added in Chapter II and some effort has been invested in the search for mistakes and unclear passages in the first edition. The central objective of the book, expressed in the title "Local Quantum Physics", is the synthesis between special relativity and quantum theory to gether with a few other principles of general nature.
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The Theory of Quantum Information

Author: John Watrous

Publisher: N.A

ISBN: 1107180562

Category: Computers

Page: 598

View: 562

Formal development of the mathematical theory of quantum information with clear proofs and exercises. For graduate students and researchers.
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Holographic Entanglement Entropy

Author: Mukund Rangamani,Tadashi Takayanagi

Publisher: Springer

ISBN: 3319525735

Category: Science

Page: 246

View: 3277

This book provides a comprehensive overview of developments in the field of holographic entanglement entropy. Within the context of the AdS/CFT correspondence, it is shown how quantum entanglement is computed by the area of certain extremal surfaces. The general lessons one can learn from this connection are drawn out for quantum field theories, many-body physics, and quantum gravity. An overview of the necessary background material is provided together with a flavor of the exciting open questions that are currently being discussed. The book is divided into four main parts. In the first part, the concept of entanglement, and methods for computing it, in quantum field theories is reviewed. In the second part, an overview of the AdS/CFT correspondence is given and the holographic entanglement entropy prescription is explained. In the third part, the time-dependence of entanglement entropy in out-of-equilibrium systems, and applications to many body physics are explored using holographic methods. The last part focuses on the connection between entanglement and geometry. Known constraints on the holographic map, as well as, elaboration of entanglement being a fundamental building block of geometry are explained. The book is a useful resource for researchers and graduate students interested in string theory and holography, condensed matter and quantum information, as it tries to connect these different subjects linked by the common theme of quantum entanglement.
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The Physics of Quantum Mechanics

Author: James Binney,David Skinner

Publisher: Oxford University Press

ISBN: 0199688575

Category: Science

Page: 392

View: 340

"First published by Cappella Archive in 2008."
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Quantum Computation and Quantum Information

Author: Michael A. Nielsen,Isaac L. Chuang

Publisher: Cambridge University Press

ISBN: 9780521635035

Category: Computers

Page: 676

View: 2859

First-ever comprehensive introduction to the major new subject of quantum computing and quantum information.
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Quantum Information Theory

Mathematical Foundation

Author: Masahito Hayashi

Publisher: Springer

ISBN: 3662497255

Category: Computers

Page: 636

View: 3222

This graduate textbook provides a unified view of quantum information theory. Clearly explaining the necessary mathematical basis, it merges key topics from both information-theoretic and quantum- mechanical viewpoints and provides lucid explanations of the basic results. Thanks to this unified approach, it makes accessible such advanced topics in quantum communication as quantum teleportation, superdense coding, quantum state transmission (quantum error-correction) and quantum encryption. Since the publication of the preceding book Quantum Information: An Introduction, there have been tremendous strides in the field of quantum information. In particular, the following topics – all of which are addressed here – made seen major advances: quantum state discrimination, quantum channel capacity, bipartite and multipartite entanglement, security analysis on quantum communication, reverse Shannon theorem and uncertainty relation. With regard to the analysis of quantum security, the present book employs an improved method for the evaluation of leaked information and identifies a remarkable relation between quantum security and quantum coherence. Taken together, these two improvements allow a better analysis of quantum state transmission. In addition, various types of the newly discovered uncertainty relation are explained. Presenting a wealth of new developments, the book introduces readers to the latest advances and challenges in quantum information. To aid in understanding, each chapter is accompanied by a set of exercises and solutions.
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Quantum Information, Computation and Communication

Author: Jonathan A. Jones,Dieter Jaksch

Publisher: Cambridge University Press

ISBN: 1139510622

Category: Science

Page: N.A

View: 2088

Quantum physics allows entirely new forms of computation and cryptography, which could perform tasks currently impossible on classical devices, leading to an explosion of new algorithms, communications protocols and suggestions for physical implementations of all these ideas. As a result, quantum information has made the transition from an exotic research topic to part of mainstream undergraduate courses in physics. Based on years of teaching experience, this textbook builds from simple fundamental concepts to cover the essentials of the field. Aimed at physics undergraduate students with a basic background in quantum mechanics, it guides readers through theory and experiment, introducing all the central concepts without getting caught up in details. Worked examples and exercises make this useful as a self-study text for those who want a brief introduction before starting on more advanced books. Solutions are available online at www.cambridge.org/9781107014466.
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Quantum State Diffusion

Author: Ian Percival

Publisher: Cambridge University Press

ISBN: 9780521620079

Category: Science

Page: 184

View: 3688

The first book devoted to quantum state diffusion - suitable for graduate students and researchers.
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The Age of Entanglement

Author: Louisa Gilder

Publisher: Vintage

ISBN: 9780307270368

Category: Science

Page: 352

View: 8388

In The Age of Entanglement, Louisa Gilder brings to life one of the pivotal debates in twentieth century physics. In 1935, Albert Einstein famously showed that, according to the quantum theory, separated particles could act as if intimately connected–a phenomenon which he derisively described as “spooky action at a distance.” In that same year, Erwin Schrödinger christened this correlation “entanglement.” Yet its existence was mostly ignored until 1964, when the Irish physicist John Bell demonstrated just how strange this entanglement really was. Drawing on the papers, letters, and memoirs of the twentieth century’s greatest physicists, Gilder both humanizes and dramatizes the story by employing the scientists’ own words in imagined face-to-face dialogues. The result is a richly illuminating exploration of one of the most exciting concepts of quantum physics. From the Trade Paperback edition.
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From Classical to Quantum Mechanics

An Introduction to the Formalism, Foundations and Applications

Author: Giampiero Esposito,Giuseppe Marmo,George Sudarshan

Publisher: Cambridge University Press

ISBN: 9781139450546

Category: Science

Page: N.A

View: 8579

This 2004 textbook provides a pedagogical introduction to the formalism, foundations and applications of quantum mechanics. Part I covers the basic material which is necessary to understand the transition from classical to wave mechanics. Topics include classical dynamics, with emphasis on canonical transformations and the Hamilton-Jacobi equation, the Cauchy problem for the wave equation, Helmholtz equation and eikonal approximation, introduction to spin, perturbation theory and scattering theory. The Weyl quantization is presented in Part II, along with the postulates of quantum mechanics. Part III is devoted to topics such as statistical mechanics and black-body radiation, Lagrangian and phase-space formulations of quantum mechanics, and the Dirac equation. This book is intended for use as a textbook for beginning graduate and advanced undergraduate courses. It is self-contained and includes problems to aid the reader's understanding.
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Quantum Physics

An Introduction Based on Photons

Author: A.I Lvovsky

Publisher: Springer

ISBN: 3662565846

Category: Science

Page: 303

View: 2090

This textbook is intended to accompany a two-semester course on quantum mechanics for physics students. Along with the traditional material covered in such a course (states, operators, Schrödinger equation, hydrogen atom), it offers in-depth discussion of the Hilbert space, the nature of measurement, entanglement, and decoherence – concepts that are crucial for the understanding of quantum physics and its relation to the macroscopic world, but rarely covered in entry-level textbooks. The book uses a mathematically simple physical system – photon polarization – as the visualization tool, permitting the student to see the entangled beauty of the quantum world from the very first pages. The formal concepts of quantum physics are illustrated by examples from the forefront of modern quantum research, such as quantum communication, teleportation and nonlocality. The author adopts a Socratic pedagogy: The student is guided to develop the machinery of quantum physics independently by solving sets of carefully chosen problems. Detailed solutions are provided.
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Quantum Computing

A Gentle Introduction

Author: Eleanor G. Rieffel,Wolfgang H. Polak

Publisher: MIT Press

ISBN: 0262015064

Category: Computers

Page: 372

View: 4637

A thorough exposition of quantum computing and the underlying concepts of quantum physics, with explanations of the relevant mathematics and numerous examples.
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Quantum Entanglement !

... Spooky Action at a Distance

Author: Paul F. Kisak

Publisher: Createspace Independent Publishing Platform

ISBN: 9781530297320

Category:

Page: 628

View: 8743

Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the quantum state of each particle cannot be described independently - instead, a quantum state may be given for the system as a whole. Measurements of physical properties such as position, momentum, spin, polarization, etc., performed on entangled particles are found to be appropriately correlated. For example, if a pair of particles is generated in such a way that their total spin is known to be zero, and one particle is found to have clockwise spin on a certain axis, then the spin of the other particle, measured on the same axis, will be found to be counterclockwise; because of the nature of quantum measurement. However, this behavior gives rise to paradoxical effects: any measurement of a property of a particle can be seen as acting on that particle (e.g., by collapsing a number of superposed states); and in the case of entangled particles, such action must be on the entangled system as a whole. It thus appears that one particle of an entangled pair "knows" what measurement has been performed on the other, and with what outcome, even though there is no known means for such information to be communicated between the particles, which at the time of measurement may be separated by arbitrarily large distances. Such phenomena were the subject of a 1935 paper by Albert Einstein, Boris Podolsky, and Nathan Rosen, and several papers by Erwin Schrodinger shortly thereafter, describing what came to be known as the EPR paradox. Einstein and others considered such behavior to be impossible, as it violated the local realist view of causality (Einstein referring to it as "spooky action at a distance") and argued that the accepted formulation of quantum mechanics must therefore be incomplete. Later, however, the counterintuitive predictions of quantum mechanics were verified experimentally. Experiments have been performed involving measuring the polarization or spin of entangled particles in different directions, which - by producing violations of Bell's inequality - demonstrate statistically that the local realist view cannot be correct. This has been shown to occur even when the measurements are performed more quickly than light could travel between the sites of measurement: there is no light speed or slower influence that can pass between the entangled particles. Recent experiments have measured entangled particles within less than one one-hundredth of a percent of the travel time of light between them. According to the formalism of quantum theory, the effect of measurement happens instantly. It is not possible, however, to use this effect to transmit classical information at faster-than-light speeds Quantum entanglement is an area of extremely active research by the physics community, and its effects have been demonstrated experimentally with photons, electrons, molecules the size of buckyballs, and even small diamonds. Research is also focused on the utilization of entanglement effects in communication and computation. Some metaphysical conclusions are being discussed as to whether quantum entanglement could be the closest phenomenon that science has discovered, that could represent a 'cosmic' consciousness, for lack of better terminology. This book is a comprehensive discussion of the issues and phenomenon of quantum entanglement and some of the implications that it has on the current field of quantum mechanics. This book is designed to be a general overview of the topic and provide you with the structured knowledge to familiarize yourself with the topic at the most affordable price possible. The accuracy and knowledge is of an international viewpoint as the edited articles represent the inputs of many knowledgeable individuals and some of the most currently available general knowledge on the topic, based on the date of publication."
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Conformal Methods in General Relativity

Author: Juan A. Valiente Kroon

Publisher: Cambridge University Press

ISBN: 1316688070

Category: Science

Page: N.A

View: 2560

This book offers a systematic exposition of conformal methods and how they can be used to study the global properties of solutions to the equations of Einstein's theory of gravity. It shows that combining these ideas with differential geometry can elucidate the existence and stability of the basic solutions of the theory. Introducing the differential geometric, spinorial and PDE background required to gain a deep understanding of conformal methods, this text provides an accessible account of key results in mathematical relativity over the last thirty years, including the stability of de Sitter and Minkowski spacetimes. For graduate students and researchers, this self-contained account includes useful visual models to help the reader grasp abstract concepts and a list of further reading, making this the perfect reference companion on the topic.
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Lectures on Groups and Vector Spaces for Physicists

Author: C J Isham

Publisher: World Scientific

ISBN: 9814507296

Category: Science

Page: 228

View: 1220

These notes are the contents of a lecture course given to third year physics undergraduates at the Imperial College who are taking the theoretical physics option. The subject of “Algebra and Groups” is of considerable importance in a number of branches of modern theoretical physics, and therefore one major objective of the course is to introduce the students to the basic ideas on the subject, bearing in mind the potential applications to quantum theory. However, another equally important aim of the course is to introduce the student to the art of genuine “mathematical” thinking. The notes are therefore written in a more precise mathematical style than is usually the case in courses aimed at physics students. Quite apart from the general educational value of such an exposure to abstract thinking, it is also the case that much modern theoretical physics draws on sophisticated ideas from pure mathematics and therefore it is most important that a perspective graduate student can approach these subjects without experiencing a total culture shock! The course is divided into three parts. The first is a short introduction to general group theory, with particular emphasis being placed on the matrix Lie groups that play such a crucial role in modern theoretical physics. The second part deals with the theory of vector spaces, with particular attention being paid to the theory of Hilbert spaces and the basic analytical techniques that are needed to handle the infinite dimensional situation. The final part of the course is a short introduction to the theory of group representations and the associated theory of characters. Contents:GroupsVector SpacesGroup Representations Readership: Mathematical physicists and mathematicians.
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