Geometry Of Quantum States PDF Download
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Author | : Ingemar Bengtsson |
Publisher | : Cambridge University Press |
Total Pages | : 637 |
Release | : 2017-08-18 |
Genre | : Science |
ISBN | : 1108293492 |
Download Geometry of Quantum States Book in PDF, ePub and Kindle
Quantum information theory is a branch of science at the frontier of physics, mathematics, and information science, and offers a variety of solutions that are impossible using classical theory. This book provides a detailed introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. The second edition contains new sections and entirely new chapters: the hot topic of multipartite entanglement; in-depth discussion of the discrete structures in finite dimensional Hilbert space, including unitary operator bases, mutually unbiased bases, symmetric informationally complete generalized measurements, discrete Wigner function, and unitary designs; the Gleason and Kochen–Specker theorems; the proof of the Lieb conjecture; the measure concentration phenomenon; and the Hastings' non-additivity theorem. This richly-illustrated book will be useful to a broad audience of graduates and researchers interested in quantum information theory. Exercises follow each chapter, with hints and answers supplied.
Author | : Ingemar Bengtsson |
Publisher | : Cambridge University Press |
Total Pages | : 479 |
Release | : 2007-12-06 |
Genre | : Science |
ISBN | : 1139453467 |
Download Geometry of Quantum States Book in PDF, ePub and Kindle
Quantum information theory is at the frontiers of physics, mathematics and information science, offering a variety of solutions that are impossible using classical theory. This book provides an introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. After a gentle introduction to the necessary mathematics the authors describe the geometry of quantum state spaces. Focusing on finite dimensional Hilbert spaces, they discuss the statistical distance measures and entropies used in quantum theory. The final part of the book is devoted to quantum entanglement - a non-intuitive phenomenon discovered by Schrödinger, which has become a key resource for quantum computation. This richly-illustrated book is useful to a broad audience of graduates and researchers interested in quantum information theory. Exercises follow each chapter, with hints and answers supplied.
Author | : Edoardo Ballico |
Publisher | : Springer |
Total Pages | : 173 |
Release | : 2019-03-13 |
Genre | : Science |
ISBN | : 3030061221 |
Download Quantum Physics and Geometry Book in PDF, ePub and Kindle
This book collects independent contributions on current developments in quantum information theory, a very interdisciplinary field at the intersection of physics, computer science and mathematics. Making intense use of the most advanced concepts from each discipline, the authors give in each contribution pedagogical introductions to the main concepts underlying their present research and present a personal perspective on some of the most exciting open problems. Keeping this diverse audience in mind, special efforts have been made to ensure that the basic concepts underlying quantum information are covered in an understandable way for mathematical readers, who can find there new open challenges for their research. At the same time, the volume can also be of use to physicists wishing to learn advanced mathematical tools, especially of differential and algebraic geometric nature.
Author | : Ingemar Bengtsson |
Publisher | : Cambridge University Press |
Total Pages | : 637 |
Release | : 2017-08-18 |
Genre | : Mathematics |
ISBN | : 1107026253 |
Download Geometry of Quantum States Book in PDF, ePub and Kindle
This new edition describes the space of quantum states and the theory of quantum entanglement from a geometric perspective.
Author | : Dariusz Chruscinski |
Publisher | : Springer Science & Business Media |
Total Pages | : 337 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 0817681760 |
Download Geometric Phases in Classical and Quantum Mechanics Book in PDF, ePub and Kindle
Several well-established geometric and topological methods are used in this work in an application to a beautiful physical phenomenon known as the geometric phase. This book examines the geometric phase, bringing together different physical phenomena under a unified mathematical scheme. The material is presented so that graduate students and researchers in applied mathematics and physics with an understanding of classical and quantum mechanics can handle the text.
Author | : Jan Ambjørn |
Publisher | : Cambridge University Press |
Total Pages | : 377 |
Release | : 1997-06-19 |
Genre | : Science |
ISBN | : 0521461677 |
Download Quantum Geometry Book in PDF, ePub and Kindle
Describes random geometry and applications to strings, quantum gravity, topological field theory and membrane physics.
Author | : Veeravalli S. Varadarajan |
Publisher | : |
Total Pages | : 255 |
Release | : 1970 |
Genre | : |
ISBN | : |
Download Geometry of Quantum Theory Book in PDF, ePub and Kindle
Author | : Dmitri Fursaev |
Publisher | : Springer Science & Business Media |
Total Pages | : 294 |
Release | : 2011-06-25 |
Genre | : Science |
ISBN | : 9400702051 |
Download Operators, Geometry and Quanta Book in PDF, ePub and Kindle
This book gives a detailed and self-contained introduction into the theory of spectral functions, with an emphasis on their applications to quantum field theory. All methods are illustrated with applications to specific physical problems from the forefront of current research, such as finite-temperature field theory, D-branes, quantum solitons and noncommutativity. In the first part of the book, necessary background information on differential geometry and quantization, including less standard material, is collected. The second part of the book contains a detailed description of main spectral functions and methods of their calculation. In the third part, the theory is applied to several examples (D-branes, quantum solitons, anomalies, noncommutativity). This book addresses advanced graduate students and researchers in mathematical physics with basic knowledge of quantum field theory and differential geometry. The aim is to prepare readers to use spectral functions in their own research, in particular in relation to heat kernels and zeta functions.
Author | : Ulf Leonhardt |
Publisher | : Cambridge University Press |
Total Pages | : 236 |
Release | : 1997-07-13 |
Genre | : Science |
ISBN | : 9780521497305 |
Download Measuring the Quantum State of Light Book in PDF, ePub and Kindle
Appendix A: Semiclassical approximation
Author | : José F. Cariñena |
Publisher | : Springer |
Total Pages | : 739 |
Release | : 2014-09-23 |
Genre | : Science |
ISBN | : 9401792208 |
Download Geometry from Dynamics, Classical and Quantum Book in PDF, ePub and Kindle
This book describes, by using elementary techniques, how some geometrical structures widely used today in many areas of physics, like symplectic, Poisson, Lagrangian, Hermitian, etc., emerge from dynamics. It is assumed that what can be accessed in actual experiences when studying a given system is just its dynamical behavior that is described by using a family of variables ("observables" of the system). The book departs from the principle that ''dynamics is first'' and then tries to answer in what sense the sole dynamics determines the geometrical structures that have proved so useful to describe the dynamics in so many important instances. In this vein it is shown that most of the geometrical structures that are used in the standard presentations of classical dynamics (Jacobi, Poisson, symplectic, Hamiltonian, Lagrangian) are determined, though in general not uniquely, by the dynamics alone. The same program is accomplished for the geometrical structures relevant to describe quantum dynamics. Finally, it is shown that further properties that allow the explicit description of the dynamics of certain dynamical systems, like integrability and super integrability, are deeply related to the previous development and will be covered in the last part of the book. The mathematical framework used to present the previous program is kept to an elementary level throughout the text, indicating where more advanced notions will be needed to proceed further. A family of relevant examples is discussed at length and the necessary ideas from geometry are elaborated along the text. However no effort is made to present an ''all-inclusive'' introduction to differential geometry as many other books already exist on the market doing exactly that. However, the development of the previous program, considered as the posing and solution of a generalized inverse problem for geometry, leads to new ways of thinking and relating some of the most conspicuous geometrical structures appearing in Mathematical and Theoretical Physics.