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Author: Ryan Brett Tessier Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
If Sn denotes the (2n + 1)-dimensional operator system spanned in the group C*-algebra C*(Fn) by the n generators of the free group Fn and their inverses, then the identity map in : Sn -> Sn is shown to be a pure completely positive map. Similarly, the identity map jn : NC(n) -> NC(n) on the noncommutative n-cube NC(n) in the group C_-algebra of the free product of n copies of Z2 is also shown to be pure. Further results on the purity of the reductions of the tensor product of pure completely positive maps are given. Some previously unrecorded generic features of pure completely positive linear maps are also presented, including a result on the pure extendibility of pure completely positive linear maps on operator systems with values in an injective von Neumann algebra.
Author: Ryan Brett Tessier Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
If Sn denotes the (2n + 1)-dimensional operator system spanned in the group C*-algebra C*(Fn) by the n generators of the free group Fn and their inverses, then the identity map in : Sn -> Sn is shown to be a pure completely positive map. Similarly, the identity map jn : NC(n) -> NC(n) on the noncommutative n-cube NC(n) in the group C_-algebra of the free product of n copies of Z2 is also shown to be pure. Further results on the purity of the reductions of the tensor product of pure completely positive maps are given. Some previously unrecorded generic features of pure completely positive linear maps are also presented, including a result on the pure extendibility of pure completely positive linear maps on operator systems with values in an injective von Neumann algebra.
Author: Giulio Chiribella Publisher: Springer ISBN: 9401773033 Category : Science Languages : en Pages : 525
Book Description
This book provides the first unified overview of the burgeoning research area at the interface between Quantum Foundations and Quantum Information. Topics include: operational alternatives to quantum theory, information-theoretic reconstructions of the quantum formalism, mathematical frameworks for operational theories, and device-independent features of the set of quantum correlations. Powered by the injection of fresh ideas from the field of Quantum Information and Computation, the foundations of Quantum Mechanics are in the midst of a renaissance. The last two decades have seen an explosion of new results and research directions, attracting broad interest in the scientific community. The variety and number of different approaches, however, makes it challenging for a newcomer to obtain a big picture of the field and of its high-level goals. Here, fourteen original contributions from leading experts in the field cover some of the most promising research directions that have emerged in the new wave of quantum foundations. The book is directed at researchers in physics, computer science, and mathematics and would be appropriate as the basis of a graduate course in Quantum Foundations.
Author: Abraham Berman Publisher: World Scientific ISBN: 9789812795212 Category : Mathematics Languages : en Pages : 222
Book Description
A real matrix is positive semidefinite if it can be decomposed as A = BBOC . In some applications the matrix B has to be elementwise nonnegative. If such a matrix exists, A is called completely positive. The smallest number of columns of a nonnegative matrix B such that A = BBOC is known as the cp- rank of A . This invaluable book focuses on necessary conditions and sufficient conditions for complete positivity, as well as bounds for the cp- rank. The methods are combinatorial, geometric and algebraic. The required background on nonnegative matrices, cones, graphs and Schur complements is outlined. Contents: Preliminaries: Matrix Theoretic Background; Positive Semidefinite Matrices; Nonnegative Matrices and M -Matrices; Schur Complements; Graphs; Convex Cones; The PSD Completion Problem; Complete Positivity: Definition and Basic Properties; Cones of Completely Positive Matrices; Small Matrices; Complete Positivity and the Comparison Matrix; Completely Positive Graphs; Completely Positive Matrices Whose Graphs are Not Completely Positive; Square Factorizations; Functions of Completely Positive Matrices; The CP Completion Problem; CP Rank: Definition and Basic Results; Completely Positive Matrices of a Given Rank; Completely Positive Matrices of a Given Order; When is the CP-Rank Equal to the Rank?. Readership: Upper level undergraduates, graduate students, academics and researchers interested in matrix theory."
Author: Gernot Alber Publisher: Springer ISBN: 3540446788 Category : Science Languages : en Pages : 227
Book Description
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.
Author: Benjamin Schumacher Publisher: Cambridge University Press ISBN: 1139487205 Category : Science Languages : en Pages : 483
Book Description
A new and exciting approach to the basics of quantum theory, this undergraduate textbook contains extensive discussions of conceptual puzzles and over 800 exercises and problems. Beginning with three elementary 'qubit' systems, the book develops the formalism of quantum theory, addresses questions of measurement and distinguishability, and explores the dynamics of quantum systems. In addition to the standard topics covered in other textbooks, it also covers communication and measurement, quantum entanglement, entropy and thermodynamics, and quantum information processing. This textbook gives a broad view of quantum theory by emphasizing dynamical evolution, and exploring conceptual and foundational issues. It focuses on contemporary topics, including measurement, time evolution, open systems, quantum entanglement, and the role of information.
Author: Sergiy Gnatyuk Publisher: BoD – Books on Demand ISBN: 1789231965 Category : Computers Languages : en Pages : 214
Book Description
This book explores both the state of the art and the latest developments in QKD. It describes the fundamental concepts and practical aspects of QKD from a viewpoint of information security and quantum channel efficiency improvement. The purpose of this book is to extend and update the knowledge of the readers in the dynamically changing field of QKD. The authors attempt to present in detail their results of scientific research, which is divided into two sections - Modern QKD Technologies and Quantum Channel Construction. It will be useful for researchers, engineers, graduates, and doctoral students working in quantum cryptography and information security-related areas.
Author: Masahito Hayashi Publisher: Springer Science & Business Media ISBN: 3540302654 Category : Science Languages : en Pages : 430
Book Description
This graduate-level textbook provides a unified viewpoint of quantum information theory that merges key topics from both the information-theoretic and quantum- mechanical viewpoints. The text provides a unified viewpoint of quantum information theory and lucid explanations of those basic results, so that the reader fundamentally grasps advances and challenges. This unified approach makes accessible such advanced topics in quantum communication as quantum teleportation, superdense coding, quantum state transmission (quantum error-correction), and quantum encryption.
Author: Ryan Brett Tessier
Author: Ryan Brett Tessier
Author: Vern Paulsen
Author: Giulio Chiribella
Author: Abraham Berman
Author: Gernot Alber
Author: Benjamin Schumacher
Author: Víctor M. Vega Vázquez
Author: Sergiy Gnatyuk
Author: William Arveson
Author: Masahito Hayashi