Alice And Bob Meet Banach The Interface Of Asymptotic Geometric Analysis And Quantum Information Theory

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Alice and Bob Meet Banach: The Interface of Asymptotic Geometric Analysis and Quantum Information Theory

Guillaume Aubrun,Stanisław J. Szarek
Alice and Bob Meet Banach The Interface of Asymptotic Geometric Analysis and Quantum Information Theory Book PDF

Author : Guillaume Aubrun,Stanisław J. Szarek
Publisher : American Mathematical Soc.
Page : 414 pages
File Size : 40,9 Mb
Release : 2017-08-30
Category : Functional analysis
ISBN : 9781470434687

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Alice and Bob Meet Banach: The Interface of Asymptotic Geometric Analysis and Quantum Information Theory by Guillaume Aubrun,Stanisław J. Szarek Pdf

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.

Geometry of Quantum States

Ingemar Bengtsson,Karol Życzkowski
Geometry of Quantum States Book PDF

Author : Ingemar Bengtsson,Karol Życzkowski
Publisher : Cambridge University Press
Page : 637 pages
File Size : 47,6 Mb
Release : 2017-08-18
Category : Mathematics
ISBN : 9781107026254

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Geometry of Quantum States by Ingemar Bengtsson,Karol Życzkowski Pdf

This new edition describes the space of quantum states and the theory of quantum entanglement from a geometric perspective.

Quantum Systems, Channels, Information

Alexander S. Holevo
Quantum Systems Channels Information Book PDF

Author : Alexander S. Holevo
Publisher : Walter de Gruyter GmbH & Co KG
Page : 366 pages
File Size : 40,7 Mb
Release : 2019-07-08
Category : Science
ISBN : 9783110642490

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Quantum Systems, Channels, Information by Alexander S. Holevo Pdf

Written by one of the founding fathers of Quantum Information, this book gives an accessible (albeit mathematically rigorous), self-contained introduction to quantum information theory. The central role is played by the concept of quantum channel and its entropic and information characteristics. In this revised edition, the main results have been updated to reflect the most recent developments in this very active field of research.

Model Theory of Operator Algebras

Isaac Goldbring
Model Theory of Operator Algebras Book PDF

Author : Isaac Goldbring
Publisher : Walter de Gruyter GmbH & Co KG
Page : 498 pages
File Size : 51,5 Mb
Release : 2023-07-24
Category : Mathematics
ISBN : 9783110768282

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Model Theory of Operator Algebras by Isaac Goldbring Pdf

Continuous model theory is an extension of classical first order logic which is best suited for classes of structures which are endowed with a metric. Applications have grown considerably in the past decade. This book is dedicated to showing how the techniques of continuous model theory are used to study C*-algebras and von Neumann algebras. This book geared to researchers in both logic and functional analysis provides the first self-contained collection of articles surveying the many applications of continuous logic to operator algebras that have been obtained in the last 15 years.

Asymptotic Geometric Analysis

Monika Ludwig,Vitali D. Milman,Vladimir Pestov,Nicole Tomczak-Jaegermann
Asymptotic Geometric Analysis Book PDF

Author : Monika Ludwig,Vitali D. Milman,Vladimir Pestov,Nicole Tomczak-Jaegermann
Publisher : Springer Science & Business Media
Page : 402 pages
File Size : 50,7 Mb
Release : 2013-03-27
Category : Mathematics
ISBN : 9781461464068

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Asymptotic Geometric Analysis by Monika Ludwig,Vitali D. Milman,Vladimir Pestov,Nicole Tomczak-Jaegermann Pdf

Asymptotic Geometric Analysis is concerned with the geometric and linear properties of finite dimensional objects, normed spaces, and convex bodies, especially with the asymptotics of their various quantitative parameters as the dimension tends to infinity. The deep geometric, probabilistic, and combinatorial methods developed here are used outside the field in many areas of mathematics and mathematical sciences. The Fields Institute Thematic Program in the Fall of 2010 continued an established tradition of previous large-scale programs devoted to the same general research direction. The main directions of the program included: * Asymptotic theory of convexity and normed spaces * Concentration of measure and isoperimetric inequalities, optimal transportation approach * Applications of the concept of concentration * Connections with transformation groups and Ramsey theory * Geometrization of probability * Random matrices * Connection with asymptotic combinatorics and complexity theory These directions are represented in this volume and reflect the present state of this important area of research. It will be of benefit to researchers working in a wide range of mathematical sciences—in particular functional analysis, combinatorics, convex geometry, dynamical systems, operator algebras, and computer science.

Quantum Computing: From Alice to Bob

Alice Flarend,Robert Hilborn
Quantum Computing From Alice to Bob Book PDF

Author : Alice Flarend,Robert Hilborn
Publisher : Oxford University Press
Page : 304 pages
File Size : 43,9 Mb
Release : 2022-03-21
Category : Science
ISBN : 9780192672704

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Quantum Computing: From Alice to Bob by Alice Flarend,Robert Hilborn Pdf

Quantum Computing: From Alice to Bob provides a distinctive and accessible introduction to the rapidly growing fields of quantum information science and quantum computing. The textbook is designed for undergraduate students and upper-level secondary school students with little or no background in physics, computer science, or mathematics beyond secondary school algebra and a bit of trigonometry. Higher education faculty members and secondary school mathematics, physics, and computer science educators who want to learn about quantum computing and perhaps teach a course accessible to students with wide-ranging backgrounds will also find the book useful and enjoyable. While broadly accessible, the textbook also provides a solid conceptual and formal understanding of quantum states and entanglement - the key ingredients in quantum computing. The authors dish up a hearty meal for the readers, disentangling and explaining many of the classic quantum algorithms that demonstrate how and when QC has an advantage over classical computers. The book is spiced with Try Its, brief exercises that engage the readers in problem solving (both with and without mathematics) and help them digest the many counter-intuitive quantum information science and quantum computing concepts.

Foundations of Quantum Theory

Klaas Landsman
Foundations of Quantum Theory Book PDF

Author : Klaas Landsman
Publisher : Unknown
Page : 880 pages
File Size : 44,7 Mb
Release : 2020-10-09
Category : Science
ISBN : 1013278364

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Foundations of Quantum Theory by Klaas Landsman Pdf

This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.

Asymptotic Geometric Analysis, Part I

Shiri Artstein-Avidan, Apostolos Giannopoulos, Vitali D. Milman
Asymptotic Geometric Analysis Part I Book PDF

Author : Shiri Artstein-Avidan, Apostolos Giannopoulos, Vitali D. Milman
Publisher : American Mathematical Soc.
Page : 451 pages
File Size : 48,7 Mb
Release : 2015-06-18
Category : Functional analysis
ISBN : 9781470421939

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Asymptotic Geometric Analysis, Part I by Shiri Artstein-Avidan, Apostolos Giannopoulos, Vitali D. Milman Pdf

The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomenon", one of the most powerful tools of the theory, responsible for many counterintuitive results. A central theme in this book is the interaction of randomness and pattern. At first glance, life in high dimension seems to mean the existence of multiple "possibilities", so one may expect an increase in the diversity and complexity as dimension increases. However, the concentration of measure and effects caused by convexity show that this diversity is compensated and order and patterns are created for arbitrary convex bodies in the mixture caused by high dimensionality. The book is intended for graduate students and researchers who want to learn about this exciting subject. Among the topics covered in the book are convexity, concentration phenomena, covering numbers, Dvoretzky-type theorems, volume distribution in convex bodies, and more.

Lectures on the Combinatorics of Free Probability

Alexandru Nica,Roland Speicher
Lectures on the Combinatorics of Free Probability Book PDF

Author : Alexandru Nica,Roland Speicher
Publisher : Cambridge University Press
Page : 430 pages
File Size : 50,5 Mb
Release : 2006-09-07
Category : Mathematics
ISBN : 9780521858526

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Lectures on the Combinatorics of Free Probability by Alexandru Nica,Roland Speicher Pdf

This 2006 book is a self-contained introduction to free probability theory suitable for an introductory graduate level course.

Quantum Information Theory

Mark Wilde
Quantum Information Theory Book PDF

Author : Mark Wilde
Publisher : Cambridge University Press
Page : 673 pages
File Size : 51,9 Mb
Release : 2013-04-18
Category : Computers
ISBN : 9781107034259

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Quantum Information Theory by Mark Wilde Pdf

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

The Random Matrix Theory of the Classical Compact Groups

Elizabeth S. Meckes
The Random Matrix Theory of the Classical Compact Groups Book PDF

Author : Elizabeth S. Meckes
Publisher : Cambridge University Press
Page : 225 pages
File Size : 49,8 Mb
Release : 2019-08
Category : Mathematics
ISBN : 9781108419529

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The Random Matrix Theory of the Classical Compact Groups by Elizabeth S. Meckes Pdf

Provides a comprehensive introduction to the theory of random orthogonal, unitary, and symplectic matrices.

Recent Advances in Intelligent Information Systems and Applied Mathematics

Oscar Castillo,Dipak Kumar Jana,Debasis Giri,Arif Ahmed
Recent Advances in Intelligent Information Systems and Applied Mathematics Book PDF

Author : Oscar Castillo,Dipak Kumar Jana,Debasis Giri,Arif Ahmed
Publisher : Springer Nature
Page : 903 pages
File Size : 41,5 Mb
Release : 2020-01-31
Category : Technology & Engineering
ISBN : 9783030341527

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Recent Advances in Intelligent Information Systems and Applied Mathematics by Oscar Castillo,Dipak Kumar Jana,Debasis Giri,Arif Ahmed Pdf

This book describes the latest advances in intelligent techniques such as fuzzy logic, neural networks, and optimization algorithms, and their relevance in building intelligent information systems in combination with applied mathematics. The authors also outline the applications of these systems in areas like intelligent control and robotics, pattern recognition, medical diagnosis, time series prediction, and optimization of complex problems. By sharing fresh ideas and identifying new targets/problems it offers young researchers and students new directions for their future research. The book is intended for readers from mathematics and computer science, in particular professors and students working on theory and applications of intelligent systems for real-world applications.

Advances in Elliptic Curve Cryptography

Ian F. Blake,Gadiel Seroussi,Nigel P. Smart
Advances in Elliptic Curve Cryptography Book PDF

Author : Ian F. Blake,Gadiel Seroussi,Nigel P. Smart
Publisher : Cambridge University Press
Page : 299 pages
File Size : 46,6 Mb
Release : 2005-04-25
Category : Computers
ISBN : 9780521604154

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Advances in Elliptic Curve Cryptography by Ian F. Blake,Gadiel Seroussi,Nigel P. Smart Pdf

This second volume addresses tremendous progress in elliptic curve cryptography since the first volume.

Numerical Continuation Methods for Dynamical Systems

Bernd Krauskopf,Hinke M. Osinga,Jorge Galan-Vioque
Numerical Continuation Methods for Dynamical Systems Book PDF

Author : Bernd Krauskopf,Hinke M. Osinga,Jorge Galan-Vioque
Publisher : Springer
Page : 399 pages
File Size : 46,7 Mb
Release : 2007-11-06
Category : Science
ISBN : 9781402063565

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Numerical Continuation Methods for Dynamical Systems by Bernd Krauskopf,Hinke M. Osinga,Jorge Galan-Vioque Pdf

Path following in combination with boundary value problem solvers has emerged as a continuing and strong influence in the development of dynamical systems theory and its application. It is widely acknowledged that the software package AUTO - developed by Eusebius J. Doedel about thirty years ago and further expanded and developed ever since - plays a central role in the brief history of numerical continuation. This book has been compiled on the occasion of Sebius Doedel's 60th birthday. Bringing together for the first time a large amount of material in a single, accessible source, it is hoped that the book will become the natural entry point for researchers in diverse disciplines who wish to learn what numerical continuation techniques can achieve. The book opens with a foreword by Herbert B. Keller and lecture notes by Sebius Doedel himself that introduce the basic concepts of numerical bifurcation analysis. The other chapters by leading experts discuss continuation for various types of systems and objects and showcase examples of how numerical bifurcation analysis can be used in concrete applications. Topics that are treated include: interactive continuation tools, higher-dimensional continuation, the computation of invariant manifolds, and continuation techniques for slow-fast systems, for symmetric Hamiltonian systems, for spatially extended systems and for systems with delay. Three chapters review physical applications: the dynamics of a SQUID, global bifurcations in laser systems, and dynamics and bifurcations in electronic circuits.

The Craft of Probabilistic Modelling

J. Gani
The Craft of Probabilistic Modelling Book PDF

Author : J. Gani
Publisher : Springer Science & Business Media
Page : 323 pages
File Size : 47,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461386315

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The Craft of Probabilistic Modelling by J. Gani Pdf

This book brings together the personal accounts and reflections of nineteen mathematical model-builders, whose specialty is probabilistic modelling. The reader may well wonder why, apart from personal interest, one should commission and edit such a collection of articles. There are, of course, many reasons, but perhaps the three most relevant are: (i) a philosophicaJ interest in conceptual models; this is an interest shared by everyone who has ever puzzled over the relationship between thought and reality; (ii) a conviction, not unsupported by empirical evidence, that probabilistic modelling has an important contribution to make to scientific research; and finally (iii) a curiosity, historical in its nature, about the complex interplay between personal events and the development of a field of mathematical research, namely applied probability. Let me discuss each of these in turn. Philosophical Abstraction, the formation of concepts, and the construction of conceptual models present us with complex philosophical problems which date back to Democritus, Plato and Aristotle. We have all, at one time or another, wondered just how we think; are our thoughts, concepts and models of reality approxim&tions to the truth, or are they simply functional constructs helping us to master our environment? Nowhere are these problems more apparent than in mathematical model ling, where idealized concepts and constructions replace the imperfect realities for which they stand.