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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

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

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90

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320