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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

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

Statistiques

Nombre de fichiers déposés

90

Nombre de notices déposées

319