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We analyze the Google matrix of directed networks of Wikipedia articles related to eight recent Wikipedia language editions representing different cultures (English, Arabic, German, Spanish, French, Italian, Russian, Chinese). Using the reduced Google matrix algorithm, we determine relations and interactions of 23 society concepts and 17 religions represented by their respective articles for each of the eight editions. The effective Markov transitions are found to be more intense inside the two blocks of society concepts and religions while transitions between the blocks are significantly reduced. We establish five poles of influence for society concepts (Law, Society, Communism, Liberalism, Capitalism) as well as five poles for religions (Christianity, Islam, Buddhism, Hinduism, Chinese folk religion) and determine how they affect other entries. We compute inter-edition correlations for different key quantities providing a quantitative analysis of the differences or the proximity of views of the eight cultures with respect to the selected society concepts and religions.

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Quantum cloning is a fundamental protocol of quantum information theory. Perfect universal quantum cloning is prohibited by the laws of quantum mechanics, only imperfect copies being reachable. Symmetric quantum cloning is concerned with case when the quality of the clones is identical. In this work, we study the general case of $1 \to N$ asymmetric cloning, where one asks for arbitrary qualities of the clones. We characterize, for all Hilbert space dimensions and number of clones, the set of all possible clone qualities. This set is realized as the nonnegative part of the unit ball of a newly introduced norm, which we call the $\mathcal{Q}$-norm. We also provide a closed form expression for the quantum cloner achieving a given clone quality vector. Our analysis relies on the Schur-Weyl duality and on the study of the spectral properties of partially transposed permutation operators.

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In the quest for robust and universal quantum devices, the notion of simulation plays a crucial role, both from a theoretical and from an applied perspective. In this work, we go beyond the simulation of quantum channels and quantum measurements, studying what it means to simulate a collection of measurements, which we call a multimeter. To this end, we first explicitly characterize the completely positive transformations between multimeters. However, not all of these transformations correspond to valid simulations, as evidenced by the existence of maps that always prepare the same multimeter regardless of the input, which we call trash-and-prepare. We give a new definition of multimeter simulations as transformations that are triviality-preserving, i.e., when given a multimeter consisting of trivial measurements they can only produce another trivial multimeter. In the absence of a quantum ancilla, we then characterize the transformations that are triviality-preserving and the transformations that are trash-and-prepare. Finally, we use these characterizations to compare our new definition of multimeter simulation to three existing ones: classical simulations, compression of multimeters, and compatibility-preserving simulations.

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We introduce the Ising Network Opinion Formation (INOF) model and apply it for the analysis of networks of 6 Wikipedia language editions. In the model, Ising spins are placed at network nodes/articles and the steady-state opinion polarization of spins is determined from the Monte Carlo iterations in which a given spin orientation is determined by in-going links from other spins. The main consideration is done for opinion confrontation between {\it capitalism, imperialism} (blue opinion) and {\it socialism, communism} (red opinion). These nodes have fixed spin/opinion orientation while other nodes achieve their steady-state opinions in the process of Monte Carlo iterations. We find that the global network opinion favors {\it socialism, communism} for all 6 editions. The model also determines the opinion preferences for world countries and political leaders, showing good agreement with heuristic expectations. We also present results for opinion competition between {\it Christianity} and {\it Islam}, and USA Democratic and Republican parties. We argue that the INOF approach can find numerous applications for directed complex networks.

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Sujets

Google matrix Critical phenomena Matrix model Adaptive transform Quantum denoising Hilbert space Chaotic dynamics Wikipedia network 2DRank algorithm Semiclassical Clonage Chaos quantique Adaptative denoiser Community structure Many-body problem Quantum Physics quant-ph Adaptive filters 2DEAG Dynamical chaos ANDREAS BLUHM Random graphs Qubit Quantum information Calcul quantique 2DEG Quantum image processing Asymmetry Harper model Nonlinearity Wikipedia Spin Amplification Opinion formation Mécanique quantique Semi-classique Solar System Wikipedia networks Atom laser Correlation Entropy Numerical calculations Plug-and-Play Ordinateur quantique Random Chaotic systems 0375-b World trade network Structure Quantum denoiser World trade Interférence Deep learning Duality Anderson localization Wigner crystal 6470qj Adaptive signal and image representation Adaptive transformation Covariance Information quantique Social networks PageRank Localization CheiRank Information theory Unitarity Dark matter Chaos Networks Decoherence Directed networks Disordered Systems and Neural Networks cond-matdis-nn Quantum chaos Entanglement CheiRank algorithm ADMM Algebra FOS Physical sciences 7215Rn Husimi function Random matrix theory Quantum computation Aubry transition 0545Mt International trade Statistical description Cloning Super-Resolution Quantum mechanics Model Denoising Unfolding Poincare recurrences Toy model Quantum many-body interaction Complex networks 2DRank Fidelity PageRank algorithm Markov chains

Statistiques

Nombre de fichiers déposés

90

Nombre de notices déposées

319