Upper Bounds for Grothendieck Constants, Quantum Correlation Matrices and CCP Functions
This book concentrates on the famous Grothendieck inequality and the continued search for the still unknown best possible value of the real and complex Grothendieck constant (an open problem since 1953). It describes in detail the state of the art in research on this fundamental inequality, including Krivine's recent contributions, and sheds light on related questions in mathematics, physics and computer science, particularly with respect to the foundations of quantum theory and quantum information theory. Unifying the real and complex cases as much as possible, the monograph introduces the reader to a rich collection of results in functional analysis and probability. In particular, it includes a detailed, self-contained analysis of the multivariate distribution of complex Gaussian random vectors. The notion of Completely Correlation Preserving (CCP) functions plays a particularly important role in the exposition.

The prerequisites are a basic knowledge of standard functional analysis, complex analysis, probability, optimisation and some number theory and combinatorics. However, readers missing some background will be able to consult the generous bibliography, which contains numerous references to useful textbooks.

The book will be of interest to PhD students and researchers in functional analysis, complex analysis, probability, optimisation, number theory and combinatorics, in physics (particularly in relation to the foundations of quantum mechanics) and in computer science (quantum information and complexity theory).

1144968928
Upper Bounds for Grothendieck Constants, Quantum Correlation Matrices and CCP Functions
This book concentrates on the famous Grothendieck inequality and the continued search for the still unknown best possible value of the real and complex Grothendieck constant (an open problem since 1953). It describes in detail the state of the art in research on this fundamental inequality, including Krivine's recent contributions, and sheds light on related questions in mathematics, physics and computer science, particularly with respect to the foundations of quantum theory and quantum information theory. Unifying the real and complex cases as much as possible, the monograph introduces the reader to a rich collection of results in functional analysis and probability. In particular, it includes a detailed, self-contained analysis of the multivariate distribution of complex Gaussian random vectors. The notion of Completely Correlation Preserving (CCP) functions plays a particularly important role in the exposition.

The prerequisites are a basic knowledge of standard functional analysis, complex analysis, probability, optimisation and some number theory and combinatorics. However, readers missing some background will be able to consult the generous bibliography, which contains numerous references to useful textbooks.

The book will be of interest to PhD students and researchers in functional analysis, complex analysis, probability, optimisation, number theory and combinatorics, in physics (particularly in relation to the foundations of quantum mechanics) and in computer science (quantum information and complexity theory).

48.99 In Stock
Upper Bounds for Grothendieck Constants, Quantum Correlation Matrices and CCP Functions

Upper Bounds for Grothendieck Constants, Quantum Correlation Matrices and CCP Functions

by Frank Oertel
Upper Bounds for Grothendieck Constants, Quantum Correlation Matrices and CCP Functions
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Upper Bounds for Grothendieck Constants, Quantum Correlation Matrices and CCP Functions

Upper Bounds for Grothendieck Constants, Quantum Correlation Matrices and CCP Functions

by Frank Oertel

Overview

This book concentrates on the famous Grothendieck inequality and the continued search for the still unknown best possible value of the real and complex Grothendieck constant (an open problem since 1953). It describes in detail the state of the art in research on this fundamental inequality, including Krivine's recent contributions, and sheds light on related questions in mathematics, physics and computer science, particularly with respect to the foundations of quantum theory and quantum information theory. Unifying the real and complex cases as much as possible, the monograph introduces the reader to a rich collection of results in functional analysis and probability. In particular, it includes a detailed, self-contained analysis of the multivariate distribution of complex Gaussian random vectors. The notion of Completely Correlation Preserving (CCP) functions plays a particularly important role in the exposition.

The prerequisites are a basic knowledge of standard functional analysis, complex analysis, probability, optimisation and some number theory and combinatorics. However, readers missing some background will be able to consult the generous bibliography, which contains numerous references to useful textbooks.

The book will be of interest to PhD students and researchers in functional analysis, complex analysis, probability, optimisation, number theory and combinatorics, in physics (particularly in relation to the foundations of quantum mechanics) and in computer science (quantum information and complexity theory).

Product Details

ISBN-13: 9783031572012
Publisher: Springer-Verlag New York, LLC
Publication date: 09/12/2024
Series: Lecture Notes in Mathematics , #2349
Sold by: Barnes & Noble
Format: eBook
File size: 29 MB
Note: This product may take a few minutes to download.

About the Author

Frank Oertel is an Honorary Research Associate at the LSE Centre for Philosophy of Natural and Social Science (CPNSS) in London. After studying mathematics and physics at the University of Kaiserslautern-Landau (RPTU), he was a researcher at the University of Zurich, ETH Zurich and Heriot-Watt University, Edinburgh and a lecturer at University College Cork (UCC), Ireland and the University of Southampton, UK. His research interests are primarily in functional analysis, including its applications to quantum mechanics, and applications of functional and stochastic analysis to problems in financial mathematics. He has also worked as a mathematical advisor in the financial industry, including banking supervision and audit (Frankfurt, Zurich, Bonn, Munich and London).

Table of Contents

- Introduction and motivation.- Complex Gaussian random vectors and their probability law.- A quantum correlation matrix version of the Grothendieck inequality.- Powers of inner products of random vectors, uniformly distributed on the sphere.- Completely correlation preserving functions.- The real case: towards extending Krivine's approach.- The complex case: towards extending Haagerup's approach.- A summary scheme of the main result.- Concluding remarks and open problems.- References.- Index.
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