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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.

Quantum theory. --- Quantum entanglement.

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Quantum entanglement (QE) has rapidly become a subject of great interest in academia, industry, and government research institutions. This book builds on the first edition of Fundamentals of Quantum Entanglement to provide a transparent and more insightful introduction for graduate students, scientists, and engineers. It is also a highly useful education tool for those practitioners that were not aware of the physical origin of quantum entanglement: the Dirac-Wheeler-Pryce-Ward physics. The new edition includes an expansion on topics such as quantum entropy and quantum time. The book provides a direct, practical, and transparent introduction to the principles and physics of quantum entanglement. It does so whilst utilizing an interferometric approach based on Dirac-Feynman superposition probability amplitudes. Part of IOP Series in Coherent Sources, Quantum Fundamentals, and Applications.

Quantum entanglement. --- Optical physics. --- Quantum science.

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This book presents a complete study of natural orbitals in quantum impurity problems, revealing a certain simplicity in these interacting many-body problems. These systems consist of a few localized degrees of freedom that undergo strong interactions and hybridize with a larger system of free particles; they are central in the study of strongly correlated systems. In a first step, the standard non-perturbative numerical renormalization group method is employed to demonstrate the hierarchical structure of correlations unveiled by natural orbitals. This simplification brought new insights for simulating quantum impurity problems, and a new algorithm is developed to generate an optimized subset of natural orbitals independently of existing methods, going beyond their usual limitations. This algorithm is presented in detail in the book, and a careful benchmark on known results is carried out to guarantee the validity of the method. It is then used to study spatialentanglement structures under various conditions that were not accessible with previous methods, such as representing the electron bath by a realistic 2D square lattice or taking account of static disorder in the metallic host. In the last chapter, the non-interacting problem in the presence of disorder is studied through random matrix theory, reproducing some of the results presented in the previous chapters. The main original result of this chapter lies in the analytical calculation of the joint distribution of one-particle orbitals energies and amplitudes of the impurity, which makes it possible to calculate any disordered averaged local correlation functions. Starting from this result, calculations in the large-N limit are compared with numerical simulations.

Quantum physics. --- Electronics --- Quantum entanglement. --- Quantum Physics. --- Electronic Materials. --- Quantum Correlation and Entanglement. --- Materials.

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Quantum computers --- Quantum entanglement --- Feynman, Richard Phillips, - 1918-1988

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Characterizing entanglement is an important issue in quantum information, as it is considered to be a resource for many applications such as quantum key distribution or quantum metrology. One useful tool to detect and quantify entanglement are witness operators. A standard way to construct them is based on the fidelity of pure states and mathematically relies on the Schmidt decomposition of vectors. In this book a method to build entanglement witnesses using the Schmidt decomposition of operators is presented. One can show that these are strictly stronger than the fidelity witnesses. Moreover, the concept can be generalized easily to the multipartite case, and one may use it to quantify the dimensionality of entanglement. Finally, this scheme will be used to provide two algorithms that can be combined to improve given witnesses for multiparticle entanglement. About the author Sophia Denker studied physics at the University of Siegen. Now she is investigating concepts of high dimensional entanglement under the tutelage of Prof. Dr. Otfried Gühne. Her master thesis was awarded with the “Studienpreis des Landkreises Altenkirchen 2023”.

Quantum physics. --- Quantum computing. --- Quantum Physics. --- Quantum Information. --- Quantum entanglement.