Alice and Bob Meet Banach - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Alice and Bob Meet Banach write by Guillaume Aubrun. This book was released on 2024-07-29. Alice and Bob Meet Banach available in PDF, EPUB and Kindle. 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.
Alice and Bob Meet Banach
Alice and Bob Meet Banach - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Alice and Bob Meet Banach write by Guillaume Aubrun. This book was released on 2017-08-30. Alice and Bob Meet Banach available in PDF, EPUB and Kindle. 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.
Convexity from the Geometric Point of View
Convexity from the Geometric Point of View - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Convexity from the Geometric Point of View write by Vitor Balestro. This book was released on . Convexity from the Geometric Point of View available in PDF, EPUB and Kindle.
Upper Bounds for Grothendieck Constants, Quantum Correlation Matrices and CCP Functions
Upper Bounds for Grothendieck Constants, Quantum Correlation Matrices and CCP Functions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Upper Bounds for Grothendieck Constants, Quantum Correlation Matrices and CCP Functions write by Frank Oertel. This book was released on . Upper Bounds for Grothendieck Constants, Quantum Correlation Matrices and CCP Functions available in PDF, EPUB and Kindle.
The Adams Spectral Sequence for Topological Modular Forms
The Adams Spectral Sequence for Topological Modular Forms - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Adams Spectral Sequence for Topological Modular Forms write by Robert R. Bruner. This book was released on 2021-12-23. The Adams Spectral Sequence for Topological Modular Forms available in PDF, EPUB and Kindle. The connective topological modular forms spectrum, $tmf$, is in a sense initial among elliptic spectra, and as such is an important link between the homotopy groups of spheres and modular forms. A primary goal of this volume is to give a complete account, with full proofs, of the homotopy of $tmf$ and several $tmf$-module spectra by means of the classical Adams spectral sequence, thus verifying, correcting, and extending existing approaches. In the process, folklore results are made precise and generalized. Anderson and Brown-Comenetz duality, and the corresponding dualities in homotopy groups, are carefully proved. The volume also includes an account of the homotopy groups of spheres through degree 44, with complete proofs, except that the Adams conjecture is used without proof. Also presented are modern stable proofs of classical results which are hard to extract from the literature. Tools used in this book include a multiplicative spectral sequence generalizing a construction of Davis and Mahowald, and computer software which computes the cohomology of modules over the Steenrod algebra and products therein. Techniques from commutative algebra are used to make the calculation precise and finite. The $H$-infinity ring structure of the sphere and of $tmf$ are used to determine many differentials and relations.
