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.

This book is devoted to research topics in quantum entanglement at the energy frontier of particle and nuclear physics, and important interdisciplinary collaborations with colleagues from fields outside of physics. A non-exhaustive list of examples of the latter can include mathematics, computer science, social sciences, philosophy, and how physics can interact with them in a way that supports successful outcomes. These are exciting times in the field of quantum information science, with new research results and their applications in society exhibiting themselves rather frequently. But what is even more exciting is that the frequency of these new results and their applications increases with a rapidity that will motivate new methods, new theories, new experiments, and new collaborations outside of the field that future researchers will find quite challenging.

What is "topological" about topological quantum states? How many types of topological quantum phases are there? What is a zero-energy Majorana mode, how can it be realized in a solid-state system, and how can it be used as a platform for topological quantum computation? What is quantum computation and what makes it different from classical computation? Addressing these and other related questions, Introduction to Topological Quantum Matter & Quantum Computation provides an introduction to and a synthesis of a fascinating and rapidly expanding research field emerging at the crossroads of condensed matter physics, mathematics, and computer science. Providing the big picture and emphasizing two major new paradigms in condensed matter physics – quantum topology and quantum information – this book is ideal for graduate students and researchers entering this field, as it allows for the fruitful transfer of ideas amongst different areas, and includes many specific examples to help the reader understand abstract and sometimes challenging concepts. It explores the topological quantum world beyond the well-known topological insulators and superconductors and unveils the deep connections with quantum computation. It addresses key principles behind the classification of topological quantum phases and relevant mathematical concepts and discusses models of interacting and noninteracting topological systems, such as the toric code and the p-wave superconductor. The book also covers the basic properties of anyons, and aspects concerning the realization of topological states in solid state structures and cold atom systems. Topological quantum computation is also presented using a broad perspective, which includes elements of classical and quantum information theory, basic concepts in the theory of computation, such as computational models and computational complexity, examples of quantum algorithms, and key ideas underlying quantum computation with anyons. This new edition has been updated throughout, with exciting new discussions on crystalline topological phases, including higher-order topological insulators; gapless topological phases, including Weyl semimetals; periodically-driven topological insulators; and a discussion of axion electrodynamics in topological materials. Key Features: · Provides an accessible introduction to this exciting, cross-disciplinary area of research. · Fully updated throughout with new content on the latest result from the field. · Authored by an authority on the subject. Tudor Stanescu is a professor of Condensed Matter Theory at West Virginia University, USA. He received a B.S. in Physics from the University of Bucharest, Romania, in 1994 and a Ph.D. in Theoretical Physics from the University of Illinois at Urbana Champaign in 2002. He was a Postdoctoral Fellow at Rutgers University and at the University of Maryland from 2003 to 2009. He joined the Department of Physics and Astronomy at West Virginia University in Fall 2009. Prof. Stanescu’s research interests encompass a variety of topics in theoretical condensed matter physics including topological insulators and superconductors, topological quantum computation, ultra-cold atom systems in optical lattices, and strongly correlated materials, such as, for example, cuprate high-temperature superconductors. His research uses a combination of analytical and numerical tools and focuses on understanding the emergence of exotic states of matter in solid state and cold atom structures, for example, topological superconducting phases that host Majorana zero modes, and on investigating the possibilities of exploiting these states as physical platforms for quantum computation.

This book constitutes the thoroughly refereed post-conference proceedings of the 9th International Conference on Quantum Interaction, QI 2015, held in Filzbach, Switzerland, in July 2015. The 20 papers together with 2 invited keynotes presented in this book were carefully selected from 27 submissions. Quantum Interaction has developed into an emerging interdisciplinary area of science combining research topics in mathematics, physics, psychology, economics, cognitive science, and computer science.

This book contains lecture notes by world experts on topological quantum phenomena, which are being developed at unprecedented rates in novel material systems.

Recent work in quantum information science has produced a revolution in our understanding of quantum entanglement. Scientists now view entanglement as a physical resource with many important applications. These range from quantum computers, which would be able to compute exponentially faster than classical computers, to quantum cryptographic techniques, which could provide unbreakable codes for the transfer of secret information over public channels. These important advances in the study of quantum entanglement and information touch on deep foundational issues in both physics and philosophy. This interdisciplinary volume brings together fourteen of the world's leading physicists and philosophers of physics to address the most important developments and debates in this exciting area of research. It offers a broad spectrum of approaches to resolving deep foundational challenges - philosophical, mathematical, and physical - raised by quantum information, quantum processing, and entanglement. This book is ideal for historians, philosophers of science and physicists.

This book presents the up-to-date status of quantum theory and the outlook for its development in the 21st century. The covered topics include basic problems of quantum physics, with emphasis on the foundations of quantum theory, quantum computing and control, quantum optics, coherent states and Wigner functions, as well as on methods of quantum physics based on Lie groups and algebras, quantum groups and noncommutative geometry.

This book offers a thorough technical elaboration and philosophical defense of an objectivist informational interpretation of quantum mechanics according to which its novel content is located in its kinematical framework, that is, in how the theory describes systems independently of the specifics of their dynamics. It will be of interest to researchers and students in the philosophy of physics and in theoretical physics with an interest in the foundations of quantum mechanics. Additionally, parts of the book may be used as the basis for courses introducing non-physics majors to quantum mechanics, or for self-study by those outside of the university with an interest in quantum mechanics. With a Foreword by Jeffrey Bub. -- “Understanding Quantum Raffles is a wonderful book for both the specialists and those with curious minds. The elegance and the simplicity with which the 'three Mikes' explain some of the deepest aspects of quantum mechanics on the basis of probabilities and correlations are dazzling and delightful. The same elegance and simplicity also make the book ideal for any engaged reader who ever wondered what is so special about quantum mechanics. In our age of new quantum technologies, this is something anyone should read.” (Guido Bacciagaluppi, author of Quantum Theory at the Crossroads) “This book makes a sustained argument for an informational interpretation of quantum theory, blending an elegant mathematical characterisation of quantum correlations with incisive historical and philosophical analysis. A must-read for those interested in quantum foundations, and also a fertile source of teaching inspiration for quantum theory.” (Leah Henderson, Department of Theoretical Philosophy, University of Groningen) “This is one of the most fascinating and accessible presentations of the informational approach to quantum mechanics. What has so far been mostly restricted to the theoretical physics community is here masterfully explained for a broader audience even without a physics background. Scholars, students, and laypeople alike will appreciate the clear, vivid, and yet deep discussion of what raffle tickets and correlation elliptopes can tell us about the physics and philosophy of the quantum world.” (Markus Müller, Institute for Quantum Optics and Quantum Information, Vienna)