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