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Quantum Information and Foundations

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ISBN: 9783039283804 9783039283811 Year: Pages: 508 DOI: 10.3390/books978-3-03928-381-1 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2020-04-07 23:07:09
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Quantum information has dramatically changed information science and technology, looking at the quantum nature of the information carrier as a resource for building new information protocols, designing radically new communication and computation algorithms, and ultra-sensitive measurements in metrology, with a wealth of applications. From a fundamental perspective, this new discipline has led us to regard quantum theory itself as a special theory of information, and has opened routes for exploring solutions to the tension with general relativity, based, for example, on the holographic principle, on non-causal variations of the theory, or else on the powerful algorithm of the quantum cellular automaton, which has revealed new routes for exploring quantum fields theory, both as a new microscopic mechanism on the fundamental side, and as a tool for efficient physical quantum simulations for practical purposes. In this golden age of foundations, an astonishing number of new ideas, frameworks, and results, spawned by the quantum information theory experience, have revolutionized the way we think about the subject, with a new research community emerging worldwide, including scientists from computer science and mathematics.

Keywords

reconstruction of quantum theory --- entanglement --- monogamy --- quantum non-locality --- conserved informational charges --- limited information --- complementarity --- characterization of unitary group and state spaces --- algebraic quantum theory --- C*-algebra --- gelfand duality --- classical context --- bohrification --- process theory --- classical limit --- purity --- higher-order interference --- generalised probabilistic theories --- Euclidean Jordan algebras --- Pauli exclusion principle --- quantum foundations --- X-ray spectroscopy --- underground experiment --- silicon drift detector --- measurement uncertainty relations --- relative entropy --- position --- momentum --- quantum mechanics --- the measurement problem --- collapse models --- X-rays --- quantum gravity --- discrete spacetime --- causal sets --- path summation --- entropic gravity --- physical computing models --- complexity classes --- causality --- blind source separation (BSS) --- qubit pair --- exchange coupling --- entangled pure state --- unentanglement criterion --- probabilities in quantum measurements --- independence of random quantum sources --- iterant --- Clifford algebra --- matrix algebra --- braid group --- Fermion --- Dirac equation --- quantum information --- quantum computation --- semiclassical physics --- quantum control --- quantum genetic algorithm --- sampling-based learning control (SLC) --- quantum foundations --- relativity --- quantum gravity --- cluster states --- multipartite entanglement --- percolation --- Shannon information --- quantum information --- quantum measurements --- consistent histories --- incompatible frameworks --- single framework rule --- probability theory --- entropy --- quantum relative entropy --- quantum information --- quantum mechanics --- inference --- quantum measurement --- quantum estimation --- macroscopic quantum measurement --- quantum annealing --- adiabatic quantum computing --- hard problems --- Hadamard matrix --- binary optimization --- reconstruction of quantum mechanics --- conjugate systems --- Jordan algebras --- quantum correlations --- Gaussian states --- Gaussian unitary operations --- continuous-variable systems --- Wigner-friend experiment --- no-go theorem --- quantum foundations --- interpretations of quantum mechanics --- subsystem --- agent --- conservation of information --- purification --- group representations --- commuting subalgebras --- quantum walks --- Hubbard model --- Thirring model --- quantum information --- quantum foundations --- quantum theory and gravity

Quantum Probability and Randomness

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ISBN: 9783038977148 9783038977155 Year: Pages: 276 DOI: 10.3390/books978-3-03897-715-5 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Physics (General)
Added to DOAB on : 2019-04-25 16:37:17
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The last few years have been characterized by a tremendous development of quantum information and probability and their applications, including quantum computing, quantum cryptography, and quantum random generators. In spite of the successful development of quantum technology, its foundational basis is still not concrete and contains a few sandy and shaky slices. Quantum random generators are one of the most promising outputs of the recent quantum information revolution. Therefore, it is very important to reconsider the foundational basis of this project, starting with the notion of irreducible quantum randomness. Quantum probabilities present a powerful tool to model uncertainty. Interpretations of quantum probability and foundational meaning of its basic tools, starting with the Born rule, are among the topics which will be covered by this issue. Recently, quantum probability has started to play an important role in a few areas of research outside quantum physics&mdash;in particular, quantum probabilistic treatment of problems of theory of decision making under uncertainty. Such studies are also among the topics of this issue.

Keywords

quantum logic --- groups --- partially defined algebras --- quasigroups --- viable cultures --- quantum information theory --- bit commitment --- protocol --- entropy --- entanglement --- orthogonality --- quantum computation --- Gram–Schmidt process --- quantum probability --- potentiality --- complementarity --- uncertainty relations --- Copenhagen interpretation --- indefiniteness --- indeterminism --- causation --- randomness --- quantum information --- quantum dynamics --- entanglement --- algebra --- causality --- geometry --- probability --- quantum information theory --- realism --- reality --- entropy --- correlations --- qubits --- probability representation --- Bayes’ formula --- quantum entanglement --- three-qubit random states --- entanglement classes --- entanglement polytope --- anisotropic invariants --- quantum random number --- vacuum state --- maximization of quantum conditional min-entropy --- quantum logics --- quantum probability --- holistic semantics --- epistemic operations --- Bell inequalities --- algorithmic complexity --- Borel normality --- Bayesian inference --- model selection --- random numbers --- quantum-like models --- operational approach --- information interpretation of quantum theory --- social laser --- social energy --- quantum information field --- social atom --- Bose–Einstein statistics --- bandwagon effect --- social thermodynamics --- resonator of social laser --- master equation for socio-information excitations --- quantum contextuality --- Kochen–Specker sets --- MMP hypergraphs --- Greechie diagrams --- quantum foundations --- probability --- irreducible randomness --- random number generators --- quantum technology --- entanglement --- quantum-like models for social stochasticity --- contextuality

Quantum Foundations. 90 Years of Uncertainty

Authors: --- --- ---
ISBN: 9783038977544 Year: Pages: 188 DOI: 10.3390/books978-3-03897-755-1 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Physics (General) --- Science (General)
Added to DOAB on : 2019-04-05 10:34:31
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The name of Joseph Fourier is also inseparable from the study of the mathematics of heat. Modern research on heat equations explores the extension of the classical diffusion equation on Riemannian, sub-Riemannian manifolds, and Lie groups. In parallel, in geometric mechanics, Jean-Marie Souriau interpreted the temperature vector of Planck as a space-time vector, obtaining, in this way, a phenomenological model of continuous media, which presents some interesting properties.

Quantum Nonlocality

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ISBN: 9783038979487 9783038979494 Year: Pages: 238 DOI: 10.3390/books978-3-03897-949-4 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Physics (General)
Added to DOAB on : 2019-06-26 08:44:06
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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.

Keywords

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

Hopf Algebras, Quantum Groups and Yang-Baxter Equations

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ISBN: 9783038973249 9783038973256 Year: Pages: 238 DOI: 10.3390/books978-3-03897-325-6 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Mathematics --- Physics (General)
Added to DOAB on : 2019-01-31 11:04:50
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The Yang-Baxter equation first appeared in theoretical physics, in a paper by the Nobel laureate C.N. Yang and in the work of R.J. Baxter in the field of Statistical Mechanics. At the 1990 International Mathematics Congress, Vladimir Drinfeld, Vaughan F. R. Jones, and Edward Witten were awarded Fields Medals for their work related to the Yang-Baxter equation. It turned out that this equation is one of the basic equations in mathematical physics; more precisely, it is used for introducing the theory of quantum groups. It also plays a crucial role in: knot theory, braided categories, the analysis of integrable systems, non-commutative descent theory, quantum computing, non-commutative geometry, etc. Many scientists have used the axioms of various algebraic structures (quasi-triangular Hopf algebras, Yetter-Drinfeld categories, quandles, group actions, Lie (super)algebras, brace structures, (co)algebra structures, Jordan triples, Boolean algebras, relations on sets, etc.) or computer calculations (and Grobner bases) in order to produce solutions for the Yang-Baxter equation. However, the full classification of its solutions remains an open problem. At present, the study of solutions of the Yang-Baxter equation attracts the attention of a broad circle of scientists. The current volume highlights various aspects of the Yang-Baxter equation, related algebraic structures, and applications.

Harmonic Oscillators and Two-by‑two Matrices in Symmetry Problems in Physics

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ISBN: 9783038425007 9783038425014 Year: Pages: X, 360 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Mathematics
Added to DOAB on : 2017-10-02 11:58:37
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This book consists of the articles published in the special issues of this Symmetry journal based on two-by-two matrices and harmonic oscillators. The book also contains additional articles published by the guest editor in this Symmetry journal. They are of course based on harmonic oscillators and/or two-by-two matrices. The subject of symmetry is based on exactly soluble problems in physics, and the physical theory is not soluble unless it is based on oscillators and/or two-by-two matrices. The authors of those two special issues were aware of this environment when they submitted their articles. This book could therefore serve as an example to illustrate this important aspect of symmetry problems in physics.

Advances in Organic Conductors and Superconductors

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ISBN: 9783038971801 9783038971818 Year: Pages: 344 DOI: 10.3390/books978-3-03897-181-8 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Chemistry (General)
Added to DOAB on : 2018-10-04 12:13:06
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ca. 200 words; this text will present the book in all promotional forms (e.g. flyers). Please describe the book in straightforward and consumer-friendly terms.Crystalline conductors and superconductors based on organic molecules are a rapidly progressing field of solid-state science, comprising chemists, and experimental and theoretical physicists from all around the world. In focus are solids with electronic properties governed by delocalized π-electrons. Although carbon-based materials of various shades have gained enormous interest in recent years, charge transfer salts are still paradigmatic in this field. Progress in molecular design is achieved via tiny but ingenious modifications, as well as by fundamentally different approaches. The wealth of exciting physical phenomena is unprecedented and could not have been imagined when the field took off almost half a century ago. Organic low-dimensional conductors are prime examples of Luttinger liquids, exhibit a tendency toward Fermi surface instabilities, but can also be tuned across a dimension¬a¬lity-driven phase diagram like no other system. Superconductivity comes at the border to ordered phases in the spin and charge sectors, and, at high fields, the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state is well established. The interplay between charge and magnetic order is still under debate, but electronic ferroelectricity is well established. After decades of intense search, the spin liquid state was first discovered in organic conductors when the amount of geometrical frustration and electronic correlations is just right. They drive the metal and superconductor into an insulating Mott state, solely via electron–electron interactions. However, what do we know about the effect of disorder? Can we tune the electronic properties by pressure, by light, or by field? Research is still addressing basic questions, but devices are not out of reach. These are currently open questions, as well as hot and timely topics. The present Special Issue on “Advances in Organic Conductors and Superconductors” provides a status report summarizing the progress achieved in the last five years.

Symmetry in Quantum Optics Models

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ISBN: 9783039218585 9783039218592 Year: Pages: 92 DOI: 10.3390/books978-3-03921-859-2 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Physics (General)
Added to DOAB on : 2019-12-09 16:39:37
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Prototypical quantum optics models, such as the Jaynes–Cummings, Rabi, Tavis–Cummings, and Dicke models, are commonly analyzed with diverse techniques, including analytical exact solutions, mean-field theory, exact diagonalization, and so on. Analysis of these systems strongly depends on their symmetries, ranging, e.g., from a U(1) group in the Jaynes–Cummings model to a Z2 symmetry in the full-fledged quantum Rabi model. In recent years, novel regimes of light–matter interactions, namely, the ultrastrong and deep-strong coupling regimes, have been attracting an increasing amount of interest. The quantum Rabi and Dicke models in these exotic regimes present new features, such as collapses and revivals of the population, bounces of photon-number wave packets, as well as the breakdown of the rotating-wave approximation. Symmetries also play an important role in these regimes and will additionally change depending on whether the few- or many-qubit systems considered have associated inhomogeneous or equal couplings to the bosonic mode. Moreover, there is a growing interest in proposing and carrying out quantum simulations of these models in quantum platforms such as trapped ions, superconducting circuits, and quantum photonics. In this Special Issue Reprint, we have gathered a series of articles related to symmetry in quantum optics models, including the quantum Rabi model and its symmetries, Floquet topological quantum states in optically driven semiconductors, the spin–boson model as a simulator of non-Markovian multiphoton Jaynes–Cummings models, parity-assisted generation of nonclassical states of light in circuit quantum electrodynamics, and quasiprobability distribution functions from fractional Fourier transforms.

Emergent Quantum Mechanics. David Bohm Centennial Perspectives

Authors: --- --- ---
ISBN: 9783038976165 Year: Pages: 544 DOI: 10.3390/books978-3-03897-617-2 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Physics (General) --- Science (General)
Added to DOAB on : 2019-04-05 10:34:31
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Emergent quantum mechanics explores the possibility of an ontology for quantum mechanics. The resurgence of interest in ""deeper-level"" theories for quantum phenomena challenges the standard, textbook interpretation. The book presents expert views that critically evaluate the significance—for 21st century physics—of ontological quantum mechanics, an approach that David Bohm helped pioneer. The possibility of a deterministic quantum theory was first introduced with the original de Broglie-Bohm theory, which has also been developed as Bohmian mechanics. The wide range of perspectives that were contributed to this book on the occasion of David Bohm’s centennial celebration provide ample evidence for the physical consistency of ontological quantum mechanics. The book addresses deeper-level questions such as the following: Is reality intrinsically random or fundamentally interconnected? Is the universe local or nonlocal? Might a radically new conception of reality include a form of quantum causality or quantum ontology? What is the role of the experimenter agent? As the book demonstrates, the advancement of ‘quantum ontology’—as a scientific concept—marks a clear break with classical reality. The search for quantum reality entails unconventional causal structures and non-classical ontology, which can be fully consistent with the known record of quantum observations in the laboratory.

Keywords

quantum foundations --- nonlocality --- retrocausality --- Bell’s theorem --- Bohmian mechanics --- quantum theory --- surrealistic trajectories --- Bell inequality --- quantum mechanics --- generalized Lagrangian paths --- covariant quantum gravity --- emergent space-time --- Gaussian-like solutions --- entropy and time evolution --- resonances in quantum systems --- the Friedrichs model --- complex entropy. --- Bell’s theorem --- the causal arrow of time --- retrocausality --- superdeterminism --- toy-models --- quantum ontology --- sub-quantum dynamics --- micro-constituents --- emergent space-time --- emergent quantum gravity --- entropic gravity --- black hole thermodynamics --- Stern-Gerlach --- trajectories --- spin --- Bell theorem --- fractal geometry --- p-adic metric --- singular limit --- gravity --- conspiracy --- free will --- number theory --- quantum potential --- Feynman paths --- weak values --- Bohm theory --- no-hidden-variables theorems --- observables --- measurement problem --- Bohmian mechanics --- primitive ontology --- Retrocausation --- weak values --- Stochastic Electrodynamics --- quantum mechanics --- decoherence --- interpretations --- pilot-wave theory --- Bohmian mechanics --- Born rule statistics --- measurement problem --- quantum thermodynamics --- strong coupling --- operator thermodynamic functions --- quantum theory --- de Broglie–Bohm theory --- contextuality --- atom-surface scattering --- bohmian mechanics --- matter-wave optics --- diffraction --- vortical dynamics --- Schrödinger equation --- de Broglie–Bohm theory --- nonequilibrium thermodynamics --- zero-point field --- de Broglie–Bohm interpretation of quantum mechanics --- pilot wave --- interior-boundary condition --- ultraviolet divergence --- quantum field theory --- Aharonov–Bohm effect --- physical ontology --- nomology --- interpretation --- gauge freedom --- Canonical Presentation --- relational space --- relational interpretation of quantum mechanics --- measurement problem --- non-locality --- discrete calculus --- iterant --- commutator --- diffusion constant --- Levi-Civita connection --- curvature tensor --- constraints --- Kilmister equation --- Bianchi identity --- stochastic differential equations --- Monte Carlo simulations --- Burgers equation --- Langevin equation --- fractional velocity --- interpretations of quantum mechanics --- David Bohm --- mind–body problem --- quantum holism --- fundamental irreversibility --- space-time fluctuations --- spontaneous state reduction --- Poincaré recurrence --- symplectic camel --- quantum mechanics --- Hamiltonian --- molecule interference --- matter-waves --- metrology --- magnetic deflectometry --- photochemistry --- past of the photon --- Mach–Zehnder interferometer --- Dove prism --- photon trajectory --- weak measurement --- transition probability amplitude --- atomic metastable states --- Bell’s theorem --- Bohmian mechanics --- nonlocality --- many interacting worlds --- wavefunction nodes --- bouncing oil droplets --- stochastic quantum dynamics --- de Broglie–Bohm theory --- quantum non-equilibrium --- H-theorem --- ergodicity --- ontological quantum mechanics --- objective non-signaling constraint --- quantum inaccessibility --- epistemic agent --- emergent quantum state --- self-referential dynamics --- dynamical chaos --- computational irreducibility --- undecidable dynamics --- Turing incomputability --- quantum ontology --- nonlocality --- time-symmetry --- retrocausality --- quantum causality --- conscious agent --- emergent quantum mechanics --- Bohmian mechanics --- de Broglie-Bohm theory

Symmetries of Nonlinear PDEs on Metric Graphs and Branched Networks

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ISBN: 9783039217205 9783039217212 Year: Pages: 144 DOI: 10.3390/books978-3-03921-721-2 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 16:10:12
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This Special Issue focuses on recent progress in a new area of mathematical physics and applied analysis, namely, on nonlinear partial differential equations on metric graphs and branched networks. Graphs represent a system of edges connected at one or more branching points (vertices). The connection rule determines the graph topology. When the edges can be assigned a length and the wave functions on the edges are defined in metric spaces, the graph is called a metric graph. Evolution equations on metric graphs have attracted much attention as effective tools for the modeling of particle and wave dynamics in branched structures and networks. Since branched structures and networks appear in different areas of contemporary physics with many applications in electronics, biology, material science, and nanotechnology, the development of effective modeling tools is important for the many practical problems arising in these areas. The list of important problems includes searches for standing waves, exploring of their properties (e.g., stability and asymptotic behavior), and scattering dynamics. This Special Issue is a representative sample of the works devoted to the solutions of these and other problems.

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