Properties Of Pure Completely Positive Linear Maps Of Operator Systems
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| Author | : Giulio Chiribella |
| Publisher | : Springer |
| Total Pages | : 525 |
| Release | : 2015-12-08 |
| Genre | : Science |
| ISBN | : 9401773033 |
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 | : Benjamin Schumacher |
| Publisher | : Cambridge University Press |
| Total Pages | : 483 |
| Release | : 2010-03-25 |
| Genre | : Science |
| ISBN | : 1139487205 |
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 | : Abraham Berman |
| Publisher | : World Scientific |
| Total Pages | : 222 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 9789812795212 |
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 | : William Arveson |
| Publisher | : |
| Total Pages | : 190 |
| Release | : 1972 |
| Genre | : C*-algebras |
| ISBN | : |
| Author | : Gernot Alber |
| Publisher | : Springer |
| Total Pages | : 227 |
| Release | : 2003-07-01 |
| Genre | : Science |
| ISBN | : 3540446788 |
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 | : Dorothea Bahns |
| Publisher | : Springer |
| Total Pages | : 276 |
| Release | : 2019-06-28 |
| Genre | : Mathematics |
| ISBN | : 3030130460 |
This book presents four survey articles on various aspects of open quantum systems, specifically addressing quantum Markovian processes, Feller semigroups and nonequilibrium dynamics. The contributions are based on lectures given by distinguished experts at a summer school in Göttingen, Germany. Starting from basic notions, the authors of these lecture notes accompany the reader on a journey up to the latest research, highlighting new challenges and addressing unsolved problems at the interface between mathematics and physics. Though the book is primarily addressed to graduate students, it will also be of interest to researchers.
| Author | : Sergiy Gnatyuk |
| Publisher | : BoD – Books on Demand |
| Total Pages | : 214 |
| Release | : 2018-05-30 |
| Genre | : Computers |
| ISBN | : 1789231965 |
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 | : Alessandro Aldini |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 175 |
| Release | : 2010-06-11 |
| Genre | : Computers |
| ISBN | : 364213677X |
This book presents a set of 4 papers accompanying the lectures of leading researchers given at the 10th edition of the International School on Formal Methods for the Design of Computer, Communication and Software Systems, SFM 2010, held in Bertinoro, Italy, in June 2010. SFM 2010 was devoted to formal methods for quantitative aspects of programming languages and covered several topics including probabilistic and timed models, model checking, static analysis, quantum computing, real-time and embedded systems, and security.
| Author | : Nirdosh Bhatnagar |
| Publisher | : CRC Press |
| Total Pages | : 957 |
| Release | : 2018-11-20 |
| Genre | : Computers |
| ISBN | : 1351379143 |
This two-volume set on Mathematical Principles of the Internet provides a comprehensive overview of the mathematical principles of Internet engineering. The books do not aim to provide all of the mathematical foundations upon which the Internet is based. Instead, they cover a partial panorama and the key principles. Volume 1 explores Internet engineering, while the supporting mathematics is covered in Volume 2. The chapters on mathematics complement those on the engineering episodes, and an effort has been made to make this work succinct, yet self-contained. Elements of information theory, algebraic coding theory, cryptography, Internet traffic, dynamics and control of Internet congestion, and queueing theory are discussed. In addition, stochastic networks, graph-theoretic algorithms, application of game theory to the Internet, Internet economics, data mining and knowledge discovery, and quantum computation, communication, and cryptography are also discussed. In order to study the structure and function of the Internet, only a basic knowledge of number theory, abstract algebra, matrices and determinants, graph theory, geometry, analysis, optimization theory, probability theory, and stochastic processes, is required. These mathematical disciplines are defined and developed in the books to the extent that is needed to develop and justify their application to Internet engineering.
| Author | : Masahito Hayashi |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 430 |
| Release | : 2006-04-20 |
| Genre | : Science |
| ISBN | : 3540302654 |
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.
