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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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This thesis highlights research explorations in quantum contextuality with photons. Quantum contextuality is one of the most intriguing and peculiar predictions of quantum mechanics. It is also a cornerstone in modern quantum information science. It is the origin of the famous quantum nonlocality and various nonclassical paradoxes. It is also a resource for many quantum information processing tasks and even universal quantum computing. Therefore, the study of quantum contextuality not only advances the comprehension of the foundations of quantum physics, but also facilitates the practical applications of quantum information technology. In the last fifteen years, the study of quantum contextuality has developed from a purely theoretical level to a stage where direct experimental tests become amenable. However, the experimental research on contextuality at the current stage largely focuses on direct validations of some most famous predictions of contextuality, while other forms of contextuality and its practical applications in quantum information science are rarely involved. The research in this thesis is committed to bridge this gap from two directions: (1) to construct and test stronger forms of contextuality and relieve the requirements of contextuality experiments on experimental platforms, and (2) to explore the connections between contextuality and the other concepts in quantum information science and directly demonstrate the application of contextuality in broader scenarios. Specifically, the thesis have discussed the research topics about the relationship between quantum contextuality and nonlocality, the “all-versus-nothing” paradoxes from quantum contextuality, the ore- and post-selection paradoxes from quantum contextuality, and the topological protection and braiding dynamics of quantum contextuality in quasiparticle systems.

Quantum computing. --- Quantum entanglement. --- Quantum physics. --- Computer simulation. --- Mathematical physics. --- Optics. --- Angular momentum. --- Quantum Information. --- Quantum Correlation and Entanglement. --- Quantum Simulations. --- Fundamental concepts and interpretations of QM. --- Mathematical Methods in Physics. --- Angular momentum of light.

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This book highlights the applications of continuous-variable entangled state representations in the research areas of quantum optics via the integration method within an ordered product of operators (IWOP). As a way to develop the Dirac’s symbolic method, the IWOP method has made the integration of non-commutative operators possible by arranging non-commutable operators within an ordered product symbol. It not only deals with many existent quantum optics problems but also explores new research fields. The book also establishes a theoretical framework for solving important quantum optics subjects by taking full advantage of the entangled state representations. With original methods and detailed descriptions, the book is suitable for researchers, instructors, and students interested in quantum mechanics, quantum optics, and quantum information science.

Quantum optics. --- Quantum entanglement. --- Quantum computing. --- Quantum physics. --- Quantum Optics. --- Quantum Correlation and Entanglement. --- Quantum Information. --- Quantum Physics. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Computation, Quantum --- Computing, Quantum --- Information processing, Quantum --- Quantum computation --- Quantum information processing --- Electronic data processing --- Entangled states (Quantum theory) --- Entanglement (Quantum theory) --- Quantum theory --- Optics --- Photons

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This book presents the current views of leading physicists on the bizarre property of quantum theory: nonlocality. Einstein viewed this theory as “spooky action at a distance” which, together with randomness, resulted in him being unable to accept quantum theory. The contributions in the book describe, in detail, the bizarre aspects of nonlocality, such as Einstein–Podolsky–Rosen steering and quantum teleportation—a phenomenon which cannot be explained in the framework of classical physics, due its foundations in quantum entanglement. The contributions describe the role of nonlocality in the rapidly developing field of quantum information. Nonlocal quantum effects in various systems, from solid-state quantum devices to organic molecules in proteins, are discussed. The most surprising papers in this book challenge the concept of the nonlocality of Nature, and look for possible modifications, extensions, and new formulations—from retrocausality to novel types of multiple-world theories. These attempts have not yet been fully successful, but they provide hope for modifying quantum theory according to Einstein’s vision.

Stern–Gerlach experiment --- channel entropy --- non-locality --- nonsignaling --- retro-causal channel --- communication complexity --- controlled-NOT --- Bell test --- quantum measurement --- quantum mechanics --- quantum transport --- semiconductor nanodevices --- optimization --- quantum correlation --- PR Box --- non-linear Schrödinger model --- retrocausality --- entanglement --- device-independent --- Einstein–Podolsky–Rosen argument --- quantum nonlocality --- parallel lives --- PR box --- nonlocal correlations --- hypothesis testing --- quantum bounds --- channel capacity --- Wigner-function simulations --- quantum correlations --- quantum --- pre- and post-selected systems --- local hidden variables --- density-matrix formalism --- collapse of the quantum state --- local polytope --- quantum teleportation of unknown qubit --- parity measurements --- uncertainty relations --- nonlocality --- hybrid entanglement --- selectivity filter --- p-value --- steering --- axioms for quantum theory --- no-signalling --- ion channels --- KS Box --- EPR steering --- local realism --- Non-contextuality inequality --- entropic uncertainty relation --- continuous-variable states --- nonlocal dissipation models --- Bell’s theorem --- tsallis entropy --- classical limit --- general entropies --- pigeonhole principle --- biological quantum decoherence --- discrete-variable states