The Functional Analysis Of Quantum Information Theory

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The Functional Analysis Of Quantum Information Theory

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Author : Ved Prakash Gupta
language : en
Publisher: Springer
Release Date : 2015-05-28

The Functional Analysis Of Quantum Information Theory written by Ved Prakash Gupta and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-28 with Science categories.

This book provides readers with a concise introduction to current studies on operator-algebras and their generalizations, operator spaces and operator systems, with a special focus on their application in quantum information science. This basic framework for the mathematical formulation of quantum information can be traced back to the mathematical work of John von Neumann, one of the pioneers of operator algebras, which forms the underpinning of most current mathematical treatments of the quantum theory, besides being one of the most dynamic areas of twentieth century functional analysis. Today, von Neumann’s foresight finds expression in the rapidly growing field of quantum information theory. These notes gather the content of lectures given by a very distinguished group of mathematicians and quantum information theorists, held at the IMSc in Chennai some years ago, and great care has been taken to present the material as a primer on the subject matter. Starting from the basic definitions of operator spaces and operator systems, this text proceeds to discuss several important theorems including Stinespring’s dilation theorem for completely positive maps and Kirchberg’s theorem on tensor products of C*-algebras. It also takes a closer look at the abstract characterization of operator systems and, motivated by the requirements of different tensor products in quantum information theory, the theory of tensor products in operator systems is discussed in detail. On the quantum information side, the book offers a rigorous treatment of quantifying entanglement in bipartite quantum systems, and moves on to review four different areas in which ideas from the theory of operator systems and operator algebras play a natural role: the issue of zero-error communication over quantum channels, the strong subadditivity property of quantum entropy, the different norms on quantum states and the corresponding induced norms on quantum channels, and, lastly, the applications of matrix-valued random variables in the quantum information setting.

Quantum Information Theory And Quantum Statistics

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Author : Dénes Petz
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-20

Quantum Information Theory And Quantum Statistics written by Dénes Petz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-20 with Science categories.

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.

The Theory Of Quantum Information

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Author : John Watrous
language : en
Publisher:
Release Date : 2018-04-26

The Theory Of Quantum Information written by John Watrous and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-26 with Computers categories.

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

Alice And Bob Meet Banach

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Author : Guillaume Aubrun
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-08-30

Alice And Bob Meet Banach written by Guillaume Aubrun and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-30 with Mathematics categories.

The quest to build a quantum computer is arguably one of the major scientific and technological challenges of the twenty-first century, and quantum information theory (QIT) provides the mathematical framework for that quest. Over the last dozen or so years, it has become clear that quantum information theory is closely linked to geometric functional analysis (Banach space theory, operator spaces, high-dimensional probability), a field also known as asymptotic geometric analysis (AGA). In a nutshell, asymptotic geometric analysis investigates quantitative properties of convex sets, or other geometric structures, and their approximate symmetries as the dimension becomes large. This makes it especially relevant to quantum theory, where systems consisting of just a few particles naturally lead to models whose dimension is in the thousands, or even in the billions. Alice and Bob Meet Banach is aimed at multiple audiences connected through their interest in the interface of QIT and AGA: at quantum information researchers who want to learn AGA or apply its tools; at mathematicians interested in learning QIT, or at least the part of QIT that is relevant to functional analysis/convex geometry/random matrix theory and related areas; and at beginning researchers in either field. Moreover, this user-friendly book contains numerous tables and explicit estimates, with reasonable constants when possible, which make it a useful reference even for established mathematicians generally familiar with the subject.

Quantum Information

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Author : Gernot Alber
language : en
Publisher: Springer
Release Date : 2003-07-01

Quantum Information written by Gernot Alber and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-01 with Science categories.

A self-contained introduction to the basic theoretical concepts, experimental techniques and recent advances in the fields of quantum communication, quantum information and quantum computation. The introductory and self-contained character of the contributions should make this book particularly attractive to students and active researchers in physics and computer science who want to become acquainted with the underlying basic ideas and recent advances in the rapidly evolving field of quantum information processing.

Quantum Theory For Mathematicians

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Author : Brian C. Hall
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-19

Quantum Theory For Mathematicians written by Brian C. Hall and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-19 with Science categories.

Although ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book's conversational tone as they delve into such topics as the Hilbert space approach to quantum theory; the Schrödinger equation in one space dimension; the Spectral Theorem for bounded and unbounded self-adjoint operators; the Stone–von Neumann Theorem; the Wentzel–Kramers–Brillouin approximation; the role of Lie groups and Lie algebras in quantum mechanics; and the path-integral approach to quantum mechanics. The numerous exercises at the end of each chapter make the book suitable for both graduate courses and independent study. Most of the text is accessible to graduate students in mathematics who have had a first course in real analysis, covering the basics of L2 spaces and Hilbert spaces. The final chapters introduce readers who are familiar with the theory of manifolds to more advanced topics, including geometric quantization.

Device Independent Quantum Information Processing

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Author : Rotem Arnon-Friedman
language : en
Publisher: Springer
Release Date : 2021-11-02

Device Independent Quantum Information Processing written by Rotem Arnon-Friedman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-02 with Science categories.

Device-independent quantum cryptography is a method for exchanging secret messages over potentially insecure quantum communication channels, such as optical fibers. In contrast to conventional quantum cryptography, security is guaranteed even if the devices used by the communication partners, such as photon sources and detectors, deviate from their theoretical specifications. This is of high practical relevance, for attacks to current implementations of quantum cryptography exploit exactly such deviations. Device-independent cryptography is however technologically so demanding that it looked as if experimental realizations are out of reach. In her thesis, Rotem Arnon-Friedman presents powerful information-theoretic methods to prove the security of device-independent quantum cryptography. Based on them, she is able to establish security in a parameter regime that may be experimentally achievable in the near future. Rotem Arnon-Friedman's thesis thus provides the theoretical foundations for an experimental demonstration of device-independent quantum cryptography.

Quantum Information Theory

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Author : Mark Wilde
language : en
Publisher: Cambridge University Press
Release Date : 2013-04-18

Quantum Information Theory written by Mark Wilde and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-18 with Computers categories.

A self-contained, graduate-level textbook that develops from scratch classical results as well as advances of the past decade.

Introduction To Quantum Information Science

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Author : Masahito Hayashi
language : en
Publisher: Springer
Release Date : 2014-08-22

Introduction To Quantum Information Science written by Masahito Hayashi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-22 with Computers categories.

This book presents the basics of quantum information, e.g., foundation of quantum theory, quantum algorithms, quantum entanglement, quantum entropies, quantum coding, quantum error correction and quantum cryptography. The required knowledge is only elementary calculus and linear algebra. This way the book can be understood by undergraduate students. In order to study quantum information, one usually has to study the foundation of quantum theory. This book describes it from more an operational viewpoint which is suitable for quantum information while traditional textbooks of quantum theory lack this viewpoint. The current book bases on Shor's algorithm, Grover's algorithm, Deutsch-Jozsa's algorithm as basic algorithms. To treat several topics in quantum information, this book covers several kinds of information quantities in quantum systems including von Neumann entropy. The limits of several kinds of quantum information processing are given. As important quantum protocols, this book contains quantum teleportation, quantum dense coding, quantum data compression. In particular conversion theory of entanglement via local operation and classical communication are treated too. This theory provides the quantification of entanglement, which coincides with von Neumann entropy. The next part treats the quantum hypothesis testing. The decision problem of two candidates of the unknown state are given. The asymptotic performance of this problem is characterized by information quantities. Using this result, the optimal performance of classical information transmission via noisy quantum channel is derived. Quantum information transmission via noisy quantum channel by quantum error correction are discussed too. Based on this topic, the secure quantum communication is explained. In particular, the quantification of quantum security which has not been treated in existing book is explained. This book treats quantum cryptography from a more practical viewpoint.

Classical And Quantum Information

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Author : Dan C. Marinescu
language : en
Publisher: Academic Press
Release Date : 2011-01-07

Classical And Quantum Information written by Dan C. Marinescu and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-07 with Mathematics categories.

A new discipline, Quantum Information Science, has emerged in the last two decades of the twentieth century at the intersection of Physics, Mathematics, and Computer Science. Quantum Information Processing is an application of Quantum Information Science which covers the transformation, storage, and transmission of quantum information; it represents a revolutionary approach to information processing. Classical and Quantum Information covers topics in quantum computing, quantum information theory, and quantum error correction, three important areas of quantum information processing. Quantum information theory and quantum error correction build on the scope, concepts, methodology, and techniques developed in the context of their close relatives, classical information theory and classical error correcting codes. - Presents recent results in quantum computing, quantum information theory, and quantum error correcting codes - Covers both classical and quantum information theory and error correcting codes - The last chapter of the book covers physical implementation of quantum information processing devices - Covers the mathematical formalism and the concepts in Quantum Mechanics critical for understanding the properties and the transformations of quantum information