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This volume is a collection of articles written by Professor M Ohya over the past three decades in the areas of quantum teleportation, quantum information theory, quantum computer, etc. By compiling Ohya's important works in these areas, the book serves as a useful reference for researchers who are working in these fields. Sample Chapter(s)
Introduction (109 KB)
Chapter 1: Adaptive Dynamics and Its Applications To Chaos and Npc Problem (1,633 KB)

Contents:

• Adaptive Dynamics and Its Applications
• A Stochastic Limit Approach to the SAT Problem

Quantum entropy. --- Quantum teleportation. --- Quantum theory. --- Teleportation, Quantum --- Quantum theory --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Entropy --- Statistical physics

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Quantum computing. --- Quantum entanglement. --- Quantum teleportation. --- Teleportation, Quantum --- Quantum theory --- Entangled states (Quantum theory) --- Entanglement (Quantum theory) --- Computation, Quantum --- Computing, Quantum --- Information processing, Quantum --- Quantum computation --- Quantum information processing --- Electronic data processing

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To celebrate the 25th anniversary of the seminal 1993 quantum teleportation paper, we are pleased to present research works, reviews, and stories about quantum communication, quantum entanglement, and quantum teleportation: (1) How was quantum teleportation invented? (2) Which teleportation experiments were performed at the Sapienza University in Rome? (3) Can we use joint measurements to generate nonclassical correlations? (4) How is classical sampling related to quantum entanglement? (5) How is classical communication related to a special quantum ensemble? (6) How can simplifying a quantum key distribution protocol make it insecure? (7) Can we teleport a two-qubit quantum state using a nonsymmetric channel? This book includes submissions by some of the most prominent quantum teleportation contributors, including Gilles Brassard, Francesco De Martini, Nicolas Gisin, and William K. Wootters, as well as additional researchers, all presenting their up-to-date insights regarding quantum communication.

quantum teleportation --- entanglement --- quantum channel --- quantum communication --- quantum key distribution --- semiquantum key distribution --- security --- attack --- subentropy --- GAP measure --- accessible information --- communication complexity --- quantum theory --- classical simulation of entanglement --- exact sampling --- random bit model --- entropy --- quantum measurements --- nonlocality --- photonics --- quantum information --- quantum entanglement

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"The P-NP problem is the most important open problem in computer science, if not all of mathematics. The Golden Ticket provides a nontechnical introduction to P-NP, its rich history, and its algorithmic implications for everything we do with computers and beyond. In this informative and entertaining book, Lance Fortnow traces how the problem arose during the Cold War on both sides of the Iron Curtain, and gives examples of the problem from a variety of disciplines, including economics, physics, and biology. He explores problems that capture the full difficulty of the P-NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. But difficulty also has its advantages. Hard problems allow us to safely conduct electronic commerce and maintain privacy in our online lives. The Golden Ticket explores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of the P-NP problem"--

Computer science --- NP-complete problems. --- Computer algorithms. --- Problems, NP-complete --- Computational complexity --- Algorithms --- NP-complete problems --- Computer algorithms --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- MATHEMATICS / Mathematical Analysis. --- MATHEMATICS / Linear Programming. --- MATHEMATICS / History & Philosophy. --- COMPUTERS / Programming / Algorithms. --- Facebook. --- Frenemy. --- Hamiltonian paths. --- Internet. --- Ketan Mulmuley. --- Leonid Levin. --- Martin Hellman. --- NP problem. --- NP problems. --- NP-complete. --- P versus NP problem. --- P versus NP. --- Richard Feynman. --- Steve Cook. --- Twitter. --- Urbana algorithm. --- Whitfield Diffie. --- academic work. --- algebraic geometry. --- algorithm. --- algorithms. --- approximation. --- big data. --- computational problems. --- computer science. --- computers. --- computing. --- cryptography. --- cryptosystem. --- database. --- decryption. --- digital computers. --- efficient algorithms. --- efficient computation. --- encryption. --- factoring. --- fast computers. --- graph isomorphism. --- heuristics. --- linear programming. --- mathematics. --- max-cut. --- network security. --- networking. --- new technologies. --- parallel computation. --- perebor. --- prime numbers. --- problems. --- programming. --- public-key cryptography. --- quantum computers. --- quantum computing. --- quantum cryptography. --- quantum mechanics. --- quantum physical systems. --- research community. --- secret messages. --- social networking data. --- solution. --- teleportation.

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Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein's work on Brownian motion. It is also relevant to understanding various aspects of quantum theory. This book explains diffusive motion and its relation to both nonrelativistic quantum theory and quantum field theory. It shows how diffusive motion concepts lead to a radical reexamination of the structure of mathematical analysis. The book's inspiration is Princeton University mathematics professor Edward Nelson's influential work in probability, functional analysis, nonstandard analysis, stochastic mechanics, and logic. The book can be used as a tutorial or reference, or read for pleasure by anyone interested in the role of mathematics in science. Because of the application of diffusive motion to quantum theory, it will interest physicists as well as mathematicians. The introductory chapter describes the interrelationships between the various themes, many of which were first brought to light by Edward Nelson. In his writing and conversation, Nelson has always emphasized and relished the human aspect of mathematical endeavor. In his intellectual world, there is no sharp boundary between the mathematical, the cultural, and the spiritual. It is fitting that the final chapter provides a mathematical perspective on musical theory, one that reveals an unexpected connection with some of the book's main themes.

Mathematical physics. --- Diffusion. --- Quantum theory. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Gases --- Liquids --- Separation (Technology) --- Solution (Chemistry) --- Solutions, Solid --- Matter --- Packed towers --- Semiconductor doping --- Physical mathematics --- Diffusion --- Properties --- Mathematics --- Affine space. --- Algebra. --- Axiom. --- Bell's theorem. --- Brownian motion. --- Central limit theorem. --- Classical mathematics. --- Classical mechanics. --- Clifford algebra. --- Combinatorial proof. --- Commutative property. --- Constructive quantum field theory. --- Continuum hypothesis. --- David Hilbert. --- Dimension (vector space). --- Discrete mathematics. --- Distribution (mathematics). --- Eigenfunction. --- Equation. --- Euclidean space. --- Experimental mathematics. --- Fermi–Dirac statistics. --- Feynman–Kac formula. --- First-order logic. --- Fokker–Planck equation. --- Foundations of mathematics. --- Fractal dimension. --- Gaussian process. --- Girsanov theorem. --- Gödel's incompleteness theorems. --- Hilbert space. --- Hilbert's program. --- Holomorphic function. --- Infinitesimal. --- Integer. --- Internal set theory. --- Interval (mathematics). --- Limit (mathematics). --- Mathematical induction. --- Mathematical optimization. --- Mathematical proof. --- Mathematician. --- Mathematics. --- Measurable function. --- Measure (mathematics). --- Minkowski space. --- Natural number. --- Neo-Riemannian theory. --- Non-standard analysis. --- Number theory. --- Operator algebra. --- Ornstein–Uhlenbeck process. --- Orthonormal basis. --- Perturbation theory (quantum mechanics). --- Philosophy of mathematics. --- Predicate (mathematical logic). --- Probability measure. --- Probability space. --- Probability theory. --- Probability. --- Projection (linear algebra). --- Pure mathematics. --- Pythagorean theorem. --- Quantum field theory. --- Quantum fluctuation. --- Quantum gravity. --- Quantum harmonic oscillator. --- Quantum mechanics. --- Quantum system. --- Quantum teleportation. --- Random variable. --- Real number. --- Renormalization group. --- Renormalization. --- Riemann mapping theorem. --- Riemann surface. --- Riemannian geometry. --- Riemannian manifold. --- Schrödinger equation. --- Scientific notation. --- Set (mathematics). --- Sign (mathematics). --- Sobolev inequality. --- Special relativity. --- Spectral theorem. --- Spin (physics). --- Statistical mechanics. --- Stochastic calculus. --- Stochastic differential equation. --- Tensor algebra. --- Theorem. --- Theoretical physics. --- Theory. --- Turing machine. --- Variable (mathematics). --- Von Neumann algebra. --- Wiener process. --- Wightman axioms. --- Zermelo–Fraenkel set theory.