Download or read book A Group Theoretic Approach to Quantum Information written by Masahito Hayashi and published by Springer. This book was released on 2016-10-31 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first one addressing quantum information from the viewpoint of group symmetry. Quantum systems have a group symmetrical structure. This structure enables to handle systematically quantum information processing. However, there is no other textbook focusing on group symmetry for quantum information although there exist many textbooks for group representation. After the mathematical preparation of quantum information, this book discusses quantum entanglement and its quantification by using group symmetry. Group symmetry drastically simplifies the calculation of several entanglement measures although their calculations are usually very difficult to handle. This book treats optimal information processes including quantum state estimation, quantum state cloning, estimation of group action and quantum channel etc. Usually it is very difficult to derive the optimal quantum information processes without asymptotic setting of these topics. However, group symmetry allows to derive these optimal solutions without assuming the asymptotic setting. Next, this book addresses the quantum error correcting code with the symmetric structure of Weyl-Heisenberg groups. This structure leads to understand the quantum error correcting code systematically. Finally, this book focuses on the quantum universal information protocols by using the group SU(d). This topic can be regarded as a quantum version of the Csiszar-Korner's universal coding theory with the type method. The required mathematical knowledge about group representation is summarized in the companion book, Group Representation for Quantum Theory.
Download or read book Quantum Information and Symmetry written by Wiesław Leoński and published by MDPI. This book was released on 2020-06-03 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent research in the fields related to the quantum information theory (QIT) is becoming some of the most intriguing and promising investigations in contemporary physics. Many novel QIT concepts are discussed in the literature, and the broad range of new models of quantum optics and solid-state physics have been recently considered in the context of QIT. Theideas of symmetry are widely discussed in all physical sciences, becoming keystones of various concepts and considerations, leading to novel discoveries in physics. Thus, this Special Issue is devoted to the broad range of QIT topics that are related to the ideas of symmetry. It covers a broad range of ideas that can develop upon the basic research and applications in the field of quantum information, and in general, quantum theory.
Download or read book Quantum Theory and Symmetries written by M. B. Paranjape and published by Springer Nature. This book was released on 2021 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of the CRM Conference Series is based on a carefully refereed selection of contributions presented at the "11th International Symposium on Quantum Theory and Symmetries", held in Montreal, Canada from July 1-5, 2019. The main objective of the meeting was to share and make accessible new research and recent results in several branches of Theoretical and Mathematical Physics, including Algebraic Methods, Condensed Matter Physics, Cosmology and Gravitation, Integrability, Non-perturbative Quantum Field Theory, Particle Physics, Quantum Computing and Quantum Information Theory, and String/ADS-CFT. There was also a special session in honour of Decio Levi. The volume is divided into sections corresponding to the sessions held during the symposium, allowing the reader to appreciate both the homogeneity and the diversity of mathematical tools that have been applied in these subject areas. Several of the plenary speakers, who are internationally recognized experts in their fields, have contributed reviews of the main topics to complement the original contributions. .
Download or read book Symmetries in Quantum Physics written by U. Fano and published by Elsevier. This book was released on 1996-06-17 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text focuses on the physics of symmetries, developing symmetries and transformations through concrete physical examples and contexts rather than presenting the information axiomatically, mathematically, and abstractly. Readers are introduced gradually to advanced mathematical procedures, including the Wigner and Racah algebras and their applications to various symmetry groups. The book also includes some of the latest research on the use of non-invariance and non-compact groups in the consideration of relativistic and many-particle problems of atoms and nuclei.This book is an updated replacement for the text Irreducible Tensorial Sets (Academic Press, 1959). Parts A and B of the present book grew out of occasional lectures in the intervening decades at the University of Chicago, where it became neccessary to update or elaborate upon certain points. Part C has been built more recently to deal with innovations and new information in the field of mathematical physics. The book as a whole develops the subject of symmetry from a physical point of view, allowing students and researchers to gain new insight on their subject. This book can be used both as a text and as a reference by students and scientists in the field.Adapts and extends the earlier Irreducible Tensor Sets (Academic Press, 1959) to classroom useExtends to multi-particle systems and relativityIncludes problems in each chapter for homework assignmentsEmbraces the latest research on non-invariance groups
Download or read book The Theory of Symmetry Actions in Quantum Mechanics written by Gianni Cassinelli and published by Springer Science & Business Media. This book was released on 2004-10-27 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book about representing symmetry in quantum mechanics. The book is on a graduate and/or researcher level and it is written with an attempt to be concise, to respect conceptual clarity and mathematical rigor. The basic structures of quantum mechanics are used to identify the automorphism group of quantum mechanics. The main concept of a symmetry action is defined as a group homomorphism from a given group, the group of symmetries, to the automorphism group of quantum mechanics. The structure of symmetry actions is determined under the assumption that the symmetry group is a Lie group. The Galilei invariance is used to illustrate the general theory by giving a systematic presentation of a Galilei invariant elementary particle. A brief description of the Galilei invariant wave equations is also given.
Download or read book Symmetry and Quantum Mechanics written by Scott Corry and published by CRC Press. This book was released on 2016-11-25 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Structured as a dialogue between a mathematician and a physicist, Symmetry and Quantum Mechanics unites the mathematical topics of this field into a compelling and physically-motivated narrative that focuses on the central role of symmetry. Aimed at advanced undergraduate and beginning graduate students in mathematics with only a minimal background in physics, this title is also useful to physicists seeking a mathematical introduction to the subject. Part I focuses on spin, and covers such topics as Lie groups and algebras, while part II offers an account of position and momentum in the context of the representation theory of the Heisenberg group, along the way providing an informal discussion of fundamental concepts from analysis such as self-adjoint operators on Hilbert space and the Stone-von Neumann Theorem. Mathematical theory is applied to physical examples such as spin-precession in a magnetic field, the harmonic oscillator, the infinite spherical well, and the hydrogen atom.
Download or read book Characterizing Entanglement and Quantum Correlations Constrained by Symmetry written by Jordi Tura i Brugués and published by Springer. This book was released on 2016-12-16 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis focuses on the study and characterization of entanglement and nonlocal correlations constrained under symmetries. It includes original results as well as detailed methods and explanations for a number of different threads of research: positive partial transpose (PPT) entanglement in the symmetric states; a novel, experimentally friendly method to detect nonlocal correlations in many-body systems; the non-equivalence between entanglement and nonlocality; and elemental monogamies of correlations. Entanglement and nonlocal correlations constitute two fundamental resources for quantum information processing, as they allow novel tasks that are otherwise impossible in a classical scenario. However, their elusive characterization is still a central problem in quantum information theory. The main reason why such a fundamental issue remains a formidable challenge lies in the exponential growth in complexity of the Hilbert space as well as the space of multipartite correlations. Physical systems of interest, on the other hand, display symmetries that can be exploited to reduce this complexity, opening the possibility that some of these questions become tractable for such systems.
Download or read book Quantum Information Meets Quantum Matter written by Bei Zeng and published by Springer. This book was released on 2019-03-28 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book approaches condensed matter physics from the perspective of quantum information science, focusing on systems with strong interaction and unconventional order for which the usual condensed matter methods like the Landau paradigm or the free fermion framework break down. Concepts and tools in quantum information science such as entanglement, quantum circuits, and the tensor network representation prove to be highly useful in studying such systems. The goal of this book is to introduce these techniques and show how they lead to a new systematic way of characterizing and classifying quantum phases in condensed matter systems. The first part of the book introduces some basic concepts in quantum information theory which are then used to study the central topic explained in Part II: local Hamiltonians and their ground states. Part III focuses on one of the major new phenomena in strongly interacting systems, the topological order, and shows how it can essentially be defined and characterized in terms of entanglement. Part IV shows that the key entanglement structure of topological states can be captured using the tensor network representation, which provides a powerful tool in the classification of quantum phases. Finally, Part V discusses the exciting prospect at the intersection of quantum information and condensed matter physics – the unification of information and matter. Intended for graduate students and researchers in condensed matter physics, quantum information science and related fields, the book is self-contained and no prior knowledge of these topics is assumed.
Download or read book A First Course on Symmetry Special Relativity and Quantum Mechanics written by Gabor Kunstatter and published by Springer Nature. This book was released on 2020-10-19 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an in-depth and accessible description of special relativity and quantum mechanics which together form the foundation of 21st century physics. A novel aspect is that symmetry is given its rightful prominence as an integral part of this foundation. The book offers not only a conceptual understanding of symmetry, but also the mathematical tools necessary for quantitative analysis. As such, it provides a valuable precursor to more focused, advanced books on special relativity or quantum mechanics. Students are introduced to several topics not typically covered until much later in their education.These include space-time diagrams, the action principle, a proof of Noether's theorem, Lorentz vectors and tensors, symmetry breaking and general relativity. The book also provides extensive descriptions on topics of current general interest such as gravitational waves, cosmology, Bell's theorem, entanglement and quantum computing. Throughout the text, every opportunity is taken to emphasize the intimate connection between physics, symmetry and mathematics.The style remains light despite the rigorous and intensive content. The book is intended as a stand-alone or supplementary physics text for a one or two semester course for students who have completed an introductory calculus course and a first-year physics course that includes Newtonian mechanics and some electrostatics. Basic knowledge of linear algebra is useful but not essential, as all requisite mathematical background is provided either in the body of the text or in the Appendices. Interspersed through the text are well over a hundred worked examples and unsolved exercises for the student.
Download or read book Physics from Symmetry written by Jakob Schwichtenberg and published by Springer. This book was released on 2017-12-01 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook that derives the fundamental theories of physics from symmetry. It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived. As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations. Thanks to the input of readers from around the world, this second edition has been purged of typographical errors and also contains several revised sections with improved explanations.
Download or read book Quantum Information and Quantum Computing written by Mikio Nakahara and published by World Scientific. This book was released on 2013 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: The open research center project "Interdisciplinary fundamental research toward realization of a quantum computer" has been supported by the Ministry of Education, Japan for five years. This is a collection of the research outcomes by the members engaged in the project. To make the presentation self-contained, it starts with an overview by Mikio Nakahara, which serves as a concise introduction to quantum information and quantum computing. Subsequent contributions include subjects from physics, chemistry, mathematics, and information science, reflecting upon the wide variety of scientists working under this project. These contributions introduce NMR quantum computing and related techniques, number theory and coding theory, quantum error correction, photosynthesis, non-classical correlations and entanglement, neutral atom quantum computer, among others. Each of the contributions will serve as a short introduction to these cutting edge research fields.
Download or read book Symmetry and Its Breaking in Quantum Field Theory written by T. Fujita and published by Nova Publishers. This book was released on 2006 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Field theory has special complexities which may not be common to other fields of research. Symmetry and its breaking are most exotic and sometimes almost mysterious to even those who can normally understand basic physics. In this textbook, there is a focus on presenting a simple and clear picture of the symmetry and its breaking in quantum field theory.
Download or read book The Theory of Quantum Information written by John Watrous and published by . This book was released on 2018-04-26 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: Formal development of the mathematical theory of quantum information with clear proofs and exercises. For graduate students and researchers.
Download or read book Quantum Information with Continuous Variables of Atoms and Light written by N. J. Cerf and published by World Scientific. This book was released on 2007 with total page 629 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum information describes the new field which bridges quantum physics and information science. The quantum world allows for completely new architectures and protocols. While originally formulated in continuous quantum variables, the field worked almost exclusively with discrete variables, such as single photons and photon pairs. The renaissance of continuous variables came with European research consortia such as ACQUIRE (Advanced Coherent Quantum Information Research) in the late 1990s, and QUICOV (Quantum Information with Continuous Variables) from 2000OCo2003. The encouraging research results of QUICOV and the new conference series CVQIP (Continuous Variable Quantum Information Processing) triggered the idea for this book. This book presents the state of the art of quantum information with continuous quantum variables. The individual chapters discuss results achieved in QUICOV and presented at the first five CVQIP conferences from 2002OCo2006. Many world-leading scientists working on continuous variables outside Europe also contribute to the book.
Download or read book Relativistic Quantum Information written by Fabrizio Tamburini and published by . This book was released on 2020-10-12 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Relativistic quantum information is one of the most exciting fields of physics today. Not only does it open possibilities for new forms of computing but it also calls into question the peaceful coexistence between classical space-time and quantum physics with scenarios that reopen the relationships between locality and nonlocality in the foundational structure of physics. Curated by two international experts Ignazio Licata and Fabrizio Tamburini, this volume hosts a selection of particularly significant essays for the new territories, and is dedicated to the 60th anniversary of Prof. Ignazio Licata.
Download or read book Pt Symmetry In Quantum And Classical Physics written by Carl M Bender and published by World Scientific Publishing. This book was released on 2018-11-22 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'The text is easy to read because the matter is clearly explained. Symmetries are a central component of physical laws, and the PT-symmetry proves to be very interesting and fruitful. The discussion of the matter is up-to-date and self-contained. The book is recommended to students of higher courses, PhD and researchers. It is also a basic read to those who wish to have an insight into this field.'Contemporary PhysicsOriginated by the author in 1998, the field of PT (parity-time) symmetry has become an extremely active and exciting area of research. PT-symmetric quantum and classical systems have theoretical, experimental, and commercial applications, and have been the subject of many journal articles, PhD theses, conferences, and symposia. Carl Bender's work has influenced major advances in physics and generations of students.This book is an accessible entry point to PT symmetry, ideal for students and scientists looking to begin their own research projects in this field.
Download or read book Quantum Mechanics written by Walter Greiner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: Greiner's lectures, which underlie these volumes, are internationally noted for their clarity, their completeness and for the effort that he has devoted to making physics an integral whole; his enthusiasm for his science is contagious and shines through almost every page. These volumes represent only a part of a unique and Herculean effort to make all of theoretical physics accessible to the interested student. Beyond that, they are of enormous value to the professional physicist and to all others working with quantum phenomena. Again and again the reader will find that, after dipping into a particular volume to review a specific topic, he will end up browsing, caught up by often fascinating new insights and developments with which he had not previously been familiar. Having used a number of Greiner's volumes in their original German in my teaching and research at Yale, I welcome these new and revised English translations and would recommend them enthusiastically to anyone searching for a coherent overview of physics.
