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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.
Abstract During the April 2023 Brazil–China summit, the creation of a trade currency supported by the BRICS countries was proposed. Using the United Nations Comtrade database, providing the frame of the world trade network associated to 194 UN countries during the decade 2010–2020, we study a mathematical model of influence battle of three currencies, namely, the US dollar, the euro, and such a hypothetical BRICS currency. In this model, a country trade preference for one of the three currencies is determined by a multiplicative factor based on trade flows between countries and their relative weights in the global international trade. The three currency seed groups are formed by 9 eurozone countries for the euro, 5 Anglo-Saxon countries for the US dollar and the 5 BRICS countries for the new proposed currency. The countries belonging to these 3 currency seed groups trade only with their own associated currency whereas the other countries choose their preferred trade currency as a function of the trade relations with their commercial partners. The trade currency preferences of countries are determined on the basis of a Monte Carlo modeling of Ising type interactions in magnetic spin systems commonly used to model opinion formation in social networks. We adapt here these models to the world trade network analysis. The results obtained from our mathematical modeling of the structure of the global trade network show that as early as 2012 about 58% of countries would have preferred to trade with the BRICS currency, 23% with the euro and 19% with the US dollar. Our results announce favorable prospects for a dominance of the BRICS currency in international trade, if only trade relations are taken into account, whereas political and other aspects are neglected.
Background noise in many fields such as medical imaging poses significant challenges for accurate diagnosis, prompting the development of denoising algorithms. Traditional methodologies, however, often struggle to address the complexities of noisy environments in high dimensional imaging systems. This paper introduces a novel quantum-inspired approach for image denoising, drawing upon principles of quantum and condensed matter physics. Our approach views medical images as amorphous structures akin to those found in condensed matter physics and we propose an algorithm that incorporates the concept of mode resolved localization directly into the denoising process. Notably, our approach eliminates the need for hyperparameter tuning. The proposed method is a standalone algorithm with minimal manual intervention, demonstrating its potential to use quantum-based techniques in classical signal denoising. Through numerical validation, we showcase the effectiveness of our approach in addressing noise-related challenges in imaging and especially medical imaging, underscoring its relevance for possible quantum computing applications.
In this article, we investigate meandric systems having one shallow side: the arch configuration on that side has depth at most two. This class of meandric systems was introduced and extensively examined by I. P. Goulden, A. Nica, and D. Puder [Int. Math. Res. Not. IMRN 2020 (2020), 983–1034]. Shallow arch configurations are in bijection with the set of interval partitions. We study meandric systems by using moment-cumulant transforms for non-crossing and interval partitions, corresponding to the notions of free and Boolean independence, respectively, in non-commutative probability. We obtain formulas for the generating series of different classes of meandric systems with one shallow side by explicitly enumerating the simpler, irreducible objects. In addition, we propose random matrix models for the corresponding meandric polynomials, which can be described in the language of quantum information theory, in particular that of quantum channels.
We introduce and study a random matrix model of Kolmogorov-Zakharov turbulence in a nonlinear purely dynamical finite-size system with many degrees of freedom. For the case of a direct cascade, the energy and norm pumping takes place at low energy scales with absorption at high energies. For a pumping strength above a certain chaos border, a global chaotic attractor appears with a stationary energy flow through a Hamiltonian inertial energy interval. In this regime, the steady-state norm distribution is described by an algebraic decay with an exponent in agreement with the Kolmogorov-Zakharov theory. Below the chaos border, the system is located in the quasi-integrable regime similar to the Kolmogorov-Arnold-Moser theory and the turbulence is suppressed. For the inverse cascade, the system rapidly enters a strongly nonlinear regime where the weak turbulence description is invalid. We argue that such a dynamical turbulence is generic, showing that it is present in other lattice models with disorder and Anderson localization. We point out that such dynamical models can be realized in multimode optical fibers.
Sujets
Directed networks
Community structure
Anomalous diffusio
Information quantique
Anderson localisation
Qubit
Model
Anderson localization
CheiRank algorithm
Solar System
Random matrix theory
Atom laser
Markov chains
Nonlinearity
Social networks
Dynamical chaos
Aubry transition
Mécanique quantique
Super-Resolution
Quantum computation
Wikipedia network
Unfolding
Adaptive transform
Wigner crystal
Information theory
Adaptive signal and image representation
Approximation semiclassical
Google matrix
Wikipedia networks
2DEAG
Complex networks
Covariance
7215Rn
Decoherence
Ordinateur quantique
World trade network
2DRank algorithm
ANDREAS BLUHM
2DRank
FOS Physical sciences
Quantum denoising
Quantum many-body interaction
Chaotic dynamics
Unitarity
ADMM
6470qj
Random graphs
Cloning
Poincare recurrences
Entropy
PageRank algorithm
Clonage
Algorithmes quantiques
Statistical description
PageRank
Denoising
Quantum denoiser
Adaptative denoiser
Algebra
Quantum chaos
Wikipedia
Duality
Deep learning
Husimi function
2DEG
Chaos
0375-b
Anderson transition
Quantum mechanics
Matrix model
Quantum image processing
Structure
Fidelity
Random
Hilbert space
World trade
Harper model
Interférence
Semi-classique
Chaos quantique
Spin
Disordered Systems and Neural Networks cond-matdis-nn
Quantum information
International trade
CheiRank
Toy model
Opinion formation
Semiclassical
Plug-and-Play
Asymmetry
Anderson model
Amplification
Adaptive filters
Networks
Calcul quantique
Dark matter
Chaotic systems
Entanglement
0545Mt
Adaptive transformation