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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 ultrasensitive 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 noncausal 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.
reconstruction of quantum theory  entanglement  monogamy  quantum nonlocality  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  higherorder interference  generalised probabilistic theories  Euclidean Jordan algebras  Pauli exclusion principle  quantum foundations  Xray spectroscopy  underground experiment  silicon drift detector  measurement uncertainty relations  relative entropy  position  momentum  quantum mechanics  the measurement problem  collapse models  Xrays  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  samplingbased 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  continuousvariable systems  Wignerfriend experiment  nogo 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
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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—in particular, quantum probabilistic treatment of problems of theory of decision making under uncertainty. Such studies are also among the topics of this issue.
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  threequbit random states  entanglement classes  entanglement polytope  anisotropic invariants  quantum random number  vacuum state  maximization of quantum conditional minentropy  quantum logics  quantum probability  holistic semantics  epistemic operations  Bell inequalities  algorithmic complexity  Borel normality  Bayesian inference  model selection  random numbers  quantumlike 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 socioinformation excitations  quantum contextuality  Kochen–Specker sets  MMP hypergraphs  Greechie diagrams  quantum foundations  probability  irreducible randomness  random number generators  quantum technology  entanglement  quantumlike models for social stochasticity  contextuality
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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, subRiemannian manifolds, and Lie groups. In parallel, in geometric mechanics, JeanMarie Souriau interpreted the temperature vector of Planck as a spacetime vector, obtaining, in this way, a phenomenological model of continuous media, which presents some interesting properties.
uncertainty relation  Wigner–Yanase–Dyson skew information  quantum memory  Born probability rule  quantumclassical relationship  spinors in quantum and classical physics  square integrable  energy quantization  Quantum HamiltonJacobi Formalism  quantum trajectory  generalized uncertainty principle  successive measurements  minimal observable length  Rényi entropy  Tsallis entropy  deep learning  quantum computing  neuromorphic computing  high performance computing  quantum mechanics  Gleason theorem  Kochen–Specker theorem  Born rule  quantum uncertainty  quantum foundations  quantum information  continuous variables  Bohmian dynamics  entanglement indicators  linear entropy  original Bell inequality  perfect correlation/anticorrelation  qudit states  quantum bound  measure of classicality  foundations of quantum mechanics  uncertainty relations  bell inequalities  entropy  quantum computing
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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 solidstate 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 multipleworld theories. These attempts have not yet been fully successful, but they provide hope for modifying quantum theory according to Einstein’s vision.
quantum nonlocality  quantum mechanics  Stern–Gerlach experiment  quantum measurement  pre and postselected systems  retrocausal 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  nonlinear Schrödinger model  biological quantum decoherence  nonlocality  parity measurements  entanglement  pigeonhole principle  controlledNOT  semiconductor nanodevices  quantum transport  densitymatrix formalism  Wignerfunction simulations  nonlocal dissipation models  steering  entropic uncertainty relation  general entropies  Bell’s theorem  Einstein–Podolsky–Rosen argument  local hidden variables  local realism  nosignalling  parallel lives  local polytope  quantum nonlocality  communication complexity  optimization  KS Box  PR Box  Noncontextuality inequality  discretevariable states  continuousvariable states  quantum teleportation of unknown qubit  hybrid entanglement  collapse of the quantum state  quantum nonlocality  communication complexity  quantum nonlocality  Bell test  deviceindependent  pvalue  hypothesis testing  nonsignaling  EPR steering  quantum correlation  nonlocality  entanglement  uncertainty relations  nonlocality  entanglement  quantum
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The YangBaxter 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 YangBaxter 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, noncommutative descent theory, quantum computing, noncommutative geometry, etc. Many scientists have used the axioms of various algebraic structures (quasitriangular Hopf algebras, YetterDrinfeld 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 YangBaxter equation. However, the full classification of its solutions remains an open problem. At present, the study of solutions of the YangBaxter equation attracts the attention of a broad circle of scientists. The current volume highlights various aspects of the YangBaxter equation, related algebraic structures, and applications.
Quantum Group  YangBaxter equation  Hopf algebra  Rmatrix  Lie algebra  braided category  duality  sixvertex model  startriangle relation  quantum integrability  braid group  quasitriangular structure  quantum projective space  bundle
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This book consists of the articles published in the special issues of this Symmetry journal based on twobytwo 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 twobytwo 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 twobytwo 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.
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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 consumerfriendly terms.Crystalline conductors and superconductors based on organic molecules are a rapidly progressing field of solidstate science, comprising chemists, and experimental and theoretical physicists from all around the world. In focus are solids with electronic properties governed by delocalized πelectrons. Although carbonbased 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 lowdimensional conductors are prime examples of Luttinger liquids, exhibit a tendency toward Fermi surface instabilities, but can also be tuned across a dimension¬a¬litydriven 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.
molecular conductors  lowdimensional conductors  unconventional superconductor  Mott insulator  quantum spin liquids  disorder
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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, meanfield 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 fullfledged quantum Rabi model. In recent years, novel regimes of light–matter interactions, namely, the ultrastrong and deepstrong 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 photonnumber wave packets, as well as the breakdown of the rotatingwave approximation. Symmetries also play an important role in these regimes and will additionally change depending on whether the few or manyqubit 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 nonMarkovian multiphoton Jaynes–Cummings models, parityassisted generation of nonclassical states of light in circuit quantum electrodynamics, and quasiprobability distribution functions from fractional Fourier transforms.
quasiprobability distribution functions  fractional Fourier transform  reconstruction of the wave function  microwave photons  quantum entanglement  superconducting circuits  circuit quantum electrodynamics  quantum Rabi model  spinboson model  JaynesCummings model  multiphoton processes  quantum simulation  topological excitations  Floquet  dynamical mean field theory  nonequilibrium  starkeffect  semiconductors  light–matter interaction  integrable systems  global spectrum  n/a
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Emergent quantum mechanics explores the possibility of an ontology for quantum mechanics. The resurgence of interest in ""deeperlevel"" 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 BroglieBohm 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 deeperlevel 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 nonclassical ontology, which can be fully consistent with the known record of quantum observations in the laboratory.
quantum foundations  nonlocality  retrocausality  Bell’s theorem  Bohmian mechanics  quantum theory  surrealistic trajectories  Bell inequality  quantum mechanics  generalized Lagrangian paths  covariant quantum gravity  emergent spacetime  Gaussianlike solutions  entropy and time evolution  resonances in quantum systems  the Friedrichs model  complex entropy.  Bell’s theorem  the causal arrow of time  retrocausality  superdeterminism  toymodels  quantum ontology  subquantum dynamics  microconstituents  emergent spacetime  emergent quantum gravity  entropic gravity  black hole thermodynamics  SternGerlach  trajectories  spin  Bell theorem  fractal geometry  padic metric  singular limit  gravity  conspiracy  free will  number theory  quantum potential  Feynman paths  weak values  Bohm theory  nohiddenvariables theorems  observables  measurement problem  Bohmian mechanics  primitive ontology  Retrocausation  weak values  Stochastic Electrodynamics  quantum mechanics  decoherence  interpretations  pilotwave theory  Bohmian mechanics  Born rule statistics  measurement problem  quantum thermodynamics  strong coupling  operator thermodynamic functions  quantum theory  de Broglie–Bohm theory  contextuality  atomsurface scattering  bohmian mechanics  matterwave optics  diffraction  vortical dynamics  Schrödinger equation  de Broglie–Bohm theory  nonequilibrium thermodynamics  zeropoint field  de Broglie–Bohm interpretation of quantum mechanics  pilot wave  interiorboundary 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  nonlocality  discrete calculus  iterant  commutator  diffusion constant  LeviCivita 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  spacetime fluctuations  spontaneous state reduction  Poincaré recurrence  symplectic camel  quantum mechanics  Hamiltonian  molecule interference  matterwaves  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 nonequilibrium  Htheorem  ergodicity  ontological quantum mechanics  objective nonsignaling constraint  quantum inaccessibility  epistemic agent  emergent quantum state  selfreferential dynamics  dynamical chaos  computational irreducibility  undecidable dynamics  Turing incomputability  quantum ontology  nonlocality  timesymmetry  retrocausality  quantum causality  conscious agent  emergent quantum mechanics  Bohmian mechanics  de BroglieBohm theory
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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.
quantum graphs  nonlinear Schrödinger equation  standing waves  metric graphs  NLS  NLD  ground states  bound states  localized nonlinearity  nonrelativistic limit  quantum graphs  nonlinear Schrödinger equation  nodal structure  soliton  breather  sineGordon equation  Schrödinger equation  star graph  quantum graph  metric graphs  scaling limit  Kre?n formula  point interactions  metric graphs  open sets converging to metric graphs  Laplacians  norm convergence of operators  convergence of spectra  networks  nonlinear shallow water equations  nonlinear wave equations
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