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