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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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Communication complexity quantifies how difficult it is for two distant computers to evaluate a function f(X,Y), where the strings X and Y are distributed to the first and second computer respectively, under the constraint of exchanging as few bits as possible. Surprisingly, some nonlocal boxes, which are resources shared by the two computers, are so powerful that they allow to collapse communication complexity, in the sense that any Boolean function f can be correctly estimated with the exchange of only one bit of communication. The Popescu-Rohrlich (PR) box is an example of such a collapsing resource, but a comprehensive description of the set of collapsing nonlocal boxes remains elusive. In this work, we carry out an algebraic study of the structure of wirings connecting nonlocal boxes, thus defining the notion of the "product of boxes" P⊠Q, and we show related associativity and commutativity results. This gives rise to the notion of the "orbit of a box", unveiling surprising geometrical properties about the alignment and parallelism of distilled boxes. The power of this new framework is that it allows us to prove previously-reported numerical observations concerning the best way to wire consecutive boxes, and to numerically and analytically recover recently-identified noisy PR boxes that collapse communication complexity for different types of noise models.

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One of the most fundamental questions in quantum information theory is PPT-entanglement of quantum states, which is an NP-hard problem in general. In this paper, however, we prove that all PPT (π¯¯¯A⊗πB)-invariant quantum states are separable if and only if all extremal unital positive (πB,πA)-covariant maps are decomposable where πA,πB are unitary representations of a compact group and πA is irreducible. Moreover, an extremal unital positive (πB,πA)-covariant map L is decomposable if and only if L is completely positive or completely copositive. We then apply these results to prove that all PPT quantum channels of the form Φ(ρ)=aTr(ρ)dIdd+bρ+cρT+(1−a−b−c)diag(ρ) are entanglement-breaking, and that all A-BC PPT (U⊗U¯¯¯¯⊗U)-invariant tripartite quantum states are A-BC separable. The former strengthens some conclusions in [VW01,KMS20], and the latter provides a strong contrast to the fact that there exist PPT-entangled (U⊗U⊗U)-invariant tripartite Werner states [EW01] and resolves some open questions raised in [COS18].

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We study the random transverse field Ising model on a finite Cayley tree. This enables us to probe key questions arising in other important disordered quantum systems, in particular the Anderson transition and the problem of dirty bosons on the Cayley tree, or the emergence of non-ergodic properties in such systems. We numerically investigate this problem building on the cavity mean-field method complemented by state-of-the art finite-size scaling analysis. Our numerics agree very well with analytical results based on an analogy with the traveling wave problem of a branching random walk in the presence of an absorbing wall. Critical properties and finite-size corrections for the zero-temperature paramagnetic-ferromagnetic transition are studied both for constant and algebraically vanishing boundary conditions. In the later case, we reveal a regime which is reminiscent of the non-ergodic delocalized phase observed in other systems, thus shedding some light on critical issues in the context of disordered quantum systems, such as Anderson transitions, the many-body localization or disordered bosons in infinite dimensions.

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We study the entanglement entropy of a random tensor network (RTN) using tools from free probability theory. Random tensor networks are simple toy models that help the understanding of the entanglement behavior of a boundary region in the ADS/CFT context. One can think of random tensor networks are specific probabilistic models for tensors having some particular geometry dictated by a graph (or network) structure. We first introduce our model of RTN, obtained by contracting maximally entangled states (corresponding to the edges of the graph) on the tensor product of Gaussian tensors (corresponding to the vertices of the graph). We study the entanglement spectrum of the resulting random spectrum along a given bipartition of the local Hilbert spaces. We provide the limiting eigenvalue distribution of the reduced density operator of the RTN state, in the limit of large local dimension. The limit value is described via a maximum flow optimization problem in a new graph corresponding to the geometry of the RTN and the given bipartition. In the case of series-parallel graphs, we provide an explicit formula for the limiting eigenvalue distribution using classical and free multiplicative convolutions. We discuss the physical implications of our results, allowing us to go beyond the semiclassical regime without any cut assumption, specifically in terms of finite corrections to the average entanglement entropy of the RTN.

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Sujets

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

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Nombre de fichiers déposés

85

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322