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
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Author : Frank Oertel
language : en
Publisher:
Release Date : 2024
Upper Bounds For Grothendieck Constants Quantum Correlation Matrices And Ccp Functions written by Frank Oertel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024 with categories.
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).
Upper Bounds For Grothendieck Constants Quantum Correlation Matrices And Ccp Functions
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Author : Frank Oertel
language : en
Publisher: Springer Nature
Release Date : 2024-09-12
Upper Bounds For Grothendieck Constants Quantum Correlation Matrices And Ccp Functions written by Frank Oertel and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-12 with Mathematics categories.
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).
Matrix Analysis And Entrywise Positivity Preservers
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Author : Apoorva Khare
language : en
Publisher:
Release Date : 2022
Matrix Analysis And Entrywise Positivity Preservers written by Apoorva Khare and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Composition operators categories.
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.
Multidimensional Real Analysis Ii
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Author : Johannes Jisse Duistermaat
language : en
Publisher:
Release Date : 2004-05-06
Multidimensional Real Analysis Ii written by Johannes Jisse Duistermaat and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-05-06 with Mathematics categories.
Part two of the authors' comprehensive and innovative work on multidimensional real analysis. This book is based on extensive teaching experience at Utrecht University and gives a thorough account of integral analysis in multidimensional Euclidean space. It is an ideal preparation for students who wish to go on to more advanced study. The notation is carefully organized and all proofs are clean, complete and rigorous. The authors have taken care to pay proper attention to all aspects of the theory. In many respects this book presents an original treatment of the subject and it contains many results and exercises that cannot be found elsewhere. The numerous exercises illustrate a variety of applications in mathematics and physics. This combined with the exhaustive and transparent treatment of subject matter make the book ideal as either the text for a course, a source of problems for a seminar or for self study.
Foundations Of Computational Mathematics
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Author : Ronald A. DeVore
language : en
Publisher: Cambridge University Press
Release Date : 2001-05-17
Foundations Of Computational Mathematics written by Ronald A. DeVore 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 2001-05-17 with Mathematics categories.
Collection of papers by leading researchers in computational mathematics, suitable for graduate students and researchers.
Arakelov Geometry And Diophantine Applications
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Author : Emmanuel Peyre
language : en
Publisher: Springer Nature
Release Date : 2021-03-10
Arakelov Geometry And Diophantine Applications written by Emmanuel Peyre and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-10 with Mathematics categories.
Bridging the gap between novice and expert, the aim of this book is to present in a self-contained way a number of striking examples of current diophantine problems to which Arakelov geometry has been or may be applied. Arakelov geometry can be seen as a link between algebraic geometry and diophantine geometry. Based on lectures from a summer school for graduate students, this volume consists of 12 different chapters, each written by a different author. The first chapters provide some background and introduction to the subject. These are followed by a presentation of different applications to arithmetic geometry. The final part describes the recent application of Arakelov geometry to Shimura varieties and the proof of an averaged version of Colmez's conjecture. This book thus blends initiation to fundamental tools of Arakelov geometry with original material corresponding to current research. This book will be particularly useful for graduate students and researchers interested in the connections between algebraic geometry and number theory. The prerequisites are some knowledge of number theory and algebraic geometry.
Epidemiology Of Healthcare Associated Infections In Australia
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Author : Ramon Z. Shaban
language : en
Publisher: Elsevier Health Sciences
Release Date : 2021-02-26
Epidemiology Of Healthcare Associated Infections In Australia written by Ramon Z. Shaban and has been published by Elsevier Health Sciences this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-26 with Medical categories.
Endorsed by the Australasian College for Infection Prevention and Control (ACIPC) ACIPC is the peak body for infection prevention and control professionals in the Australasian region. Healthcare-associated Infections (HAIs) are a major threat to patient safety and the quality of healthcare globally. Despite this, Australia does not have a nationally coordinated program for the surveillance and reporting of HAIs. Epidemiology of Healthcare-associated Infections in Australia is Australia's first peer-reviewed, evidence-based assessment of the epidemiology of HAIs using publicly available data from hospital-acquired complications (HACs), state-based surveillance systems and peer-reviewed and grey literature sources. This important work has been compiled by some of Australia's leading infection control professionals and researchers. It will build national consensus on definitions, surveillance methodology and reporting of the incidence of HAIs. In doing so, it provides hospitals and those working in infection prevention and control an opportunity to benchmark and evaluate interventions to reduce infections and ensure transparency on reporting methods that will strengthen Australia's efforts to prevent and control HAIs. Here is a great article published in Sydney Morning Herald on the publication of Epidemiology of Healthcare-associated infections in Australia. - Collated publicly available HAI surveillance definitions from jurisdictions across Australia - Collated publicly available national HACs HAI data derived from the associated surveillance programs - Identification of the gaps in both publicly available HAI data from different sources and the lack of publicly available HAI surveillance data in one serialised title - Supporting video summarising key content
Arithmetic And Geometry Over Local Fields
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Author : Bruno Anglès
language : en
Publisher: Springer
Release Date : 2021-03-04
Arithmetic And Geometry Over Local Fields written by Bruno Anglès and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-04 with Mathematics categories.
This volume introduces some recent developments in Arithmetic Geometry over local fields. Its seven chapters are centered around two common themes: the study of Drinfeld modules and non-Archimedean analytic geometry. The notes grew out of lectures held during the research program "Arithmetic and geometry of local and global fields" which took place at the Vietnam Institute of Advanced Study in Mathematics (VIASM) from June to August 2018. The authors, leading experts in the field, have put great effort into making the text as self-contained as possible, introducing the basic tools of the subject. The numerous concrete examples and suggested research problems will enable graduate students and young researchers to quickly reach the frontiers of this fascinating branch of mathematics.
Arakelov Geometry Over Adelic Curves
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Author : Huayi Chen
language : en
Publisher: Springer
Release Date : 2020-01-30
Arakelov Geometry Over Adelic Curves written by Huayi Chen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-30 with Mathematics categories.
The purpose of this book is to build the fundament of an Arakelov theory over adelic curves in order to provide a unified framework for research on arithmetic geometry in several directions. By adelic curve is meant a field equipped with a family of absolute values parametrized by a measure space, such that the logarithmic absolute value of each non-zero element of the field is an integrable function on the measure space. In the literature, such construction has been discussed in various settings which are apparently transversal to each other. The authors first formalize the notion of adelic curves and discuss in a systematic way its algebraic covers, which are important in the study of height theory of algebraic points beyond Weil–Lang’s height theory. They then establish a theory of adelic vector bundles on adelic curves, which considerably generalizes the classic geometry of vector bundles or that of Hermitian vector bundles over an arithmetic curve. They focus on an analogue of the slope theory in the setting of adelic curves and in particular estimate the minimal slope of tensor product adelic vector bundles. Finally, by using the adelic vector bundles as a tool, a birational Arakelov geometry for projective variety over an adelic curve is developed. As an application, a vast generalization of Nakai–Moishezon’s criterion of positivity is proven in clarifying the arguments of geometric nature from several fundamental results in the classic geometry of numbers. Assuming basic knowledge of algebraic geometry and algebraic number theory, the book is almost self-contained. It is suitable for researchers in arithmetic geometry as well as graduate students focusing on these topics for their doctoral theses.