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The group symmetries inherent in quantum channels often make them tractable and applicable to various problems in quantum information theory. In this paper, we introduce natural probability distributions for covariant quantum channels. Specifically, this is achieved through the application of "twirling operations" on random quantum channels derived from the Stinespring representation that use Haar-distributed random isometries. We explore various types of group symmetries, including unitary and orthogonal covariance, hyperoctahedral covariance, diagonal orthogonal covariance (DOC), and analyze their properties related to quantum entanglement based on the model parameters. In particular, we discuss the threshold phenomenon for positive partial transpose and entanglement breaking properties, comparing thresholds among different classes of random covariant channels. Finally, we contribute to the PPT$^2$ conjecture by showing that the composition between two random DOC channels is generically entanglement breaking.
We extend the opinion formation approach to probe the world influence of economical organizations. Our opinion formation model mimics a battle between currencies within the international trade network. Based on the United Nations Comtrade database, we construct the world trade network for the years of the last decade from 2010 to 2020. We consider different core groups constituted by countries preferring to trade in a specific currency. We will consider principally two core groups, namely, five Anglo-Saxon countries that prefer to trade in US dollar and the 11 BRICS+ that prefer to trade in a hypothetical currency, hereafter called BRI, pegged to their economies. We determine the trade currency preference of the other countries via a Monte Carlo process depending on the direct transactions between the countries. The results obtained in the frame of this mathematical model show that starting from the year 2014, the majority of the world countries would have preferred to trade in BRI than USD. The Monte Carlo process reaches a steady state with three distinct groups: two groups of countries preferring to trade in whatever is the initial distribution of the trade currency preferences, one in BRI and the other in USD, and a third group of countries swinging as a whole between USD and BRI depending on the initial distribution of the trade currency preferences. We also analyze the battle between three currencies: on one hand, we consider USD, BRI and EUR, the latter currency being pegged by the core group of nine EU countries. We show that the countries preferring EUR are mainly the swing countries obtained in the frame of the two currencies model. On the other hand, we consider USD, CNY (Chinese yuan), OPE, the latter currency being pegged to the major OPEC+ economies for which we try to probe the effective economical influence within international trade. Finally, we present the reduced Google matrix description of the trade relations between the Anglo-Saxon countries and the BRICS+.
Denoising is omnipresent in image processing. It is usually addressed with algorithms relying on a set of hyperparameters that control the quality of the recovered image. Manual tuning of those parameters can be a daunting task, which calls for the development of automatic tuning methods. Given a denoising algorithm, the best set of parameters is the one that minimizes the error between denoised and ground-truth images. Clearly, this ideal approach is unrealistic, as the ground-truth images are unknown in practice. In this work, we propose unsupervised cost functions — i.e., that only require the noisy image — that allow us to reach this ideal gold standard performance. Specifically, the proposed approach makes it possible to obtain an average PSNR output within less than 1% of the best achievable PSNR.
Interacting fermions in the presence of disorder pose one of the most challenging problems in condensed matter physics, primarily due to the absence of accurate numerical tools. Our investigation delves into the intricate interplay between interaction-induced Mott insulation and disorder-driven Anderson localization in the Hubbard model subjected to a random potential. On the Cayley tree, the application of statistical dynamical mean-field theory proves adept at discerning among a metal and the two distinct insulators, Anderson or Mott. Our comprehensive analysis, accounting for subtle yet potent finite-size effects and fluctuations, yields a noteworthy finding: in the presence of disorder, we consistently observe an intervening Anderson-localized regime between the metallic and Mott insulator states. This observation intriguingly mirrors scenarios witnessed in dirty Bosons, where an insulating Bose glass phase consistently emerges between the superfluid and Mott phases.
We study coherent forward scattering (CFS) in critical disordered systems, whose eigenstates are multifractals. We give general and simple arguments that make it possible to fully characterize the dynamics of the shape and height of the CFS peak. We show that the dynamics is governed by multifractal dimensions D_1 D 1 and D_2 D 2 , which suggests that CFS could be used as an experimental probe for quantum multifractality. Our predictions are universal and numerically verified in three paradigmatic models of quantum multifractality: Power-law Random Banded Matrices (PRBM), the Ruijsenaars-Schneider ensembles (RS), and the three-dimensional kicked-rotor (3DKR). In the strong multifractal regime, we show analytically that these universal predictions exactly coincide with results from standard perturbation theory applied to the PRBM and RS models.
Sujets
Poincare recurrences
Benchmark
Solar System
Hilbert space
Dynamical chaos
2DRank
Adaptative denoiser
Duality
Random graphs
Semiclassical
Complex networks
Statistical description
CheiRank
Semi-classique
Directed networks
2DEG
Interférence
Chaotic dynamics
International trade
Entropy
Denoising
Fidelity
0545Mt
Quantum chaos
Markov chains
Community structure
Information theory
0375-b
Chaos
Random
Quantum many-body interaction
Adaptive transformation
Algebra
Atom laser
ADMM
6470qj
Approximation semiclassical
ANDREAS BLUHM
Random matrix theory
Anderson model
Cloning
PageRank algorithm
Unitarity
Nonlinearity
Wikipedia
Chaos quantique
Super-Resolution
Wigner crystal
Anderson transition
PageRank
Google matrix
Calcul quantique
Dark matter
World trade
Wikipedia network
Anderson localisation
Quantum information
Adaptive filters
Quantum denoising
Anderson localization
Deep learning
Networks
Plug-and-Play
Quantum denoiser
Ordinateur quantique
Big data
Quantum computation
Astérosismologie
Husimi function
2DEAG
Chaotic systems
Arnold diffusion
Spin
Quantum image processing
Opinion formation
Decoherence
Model
Entanglement
Adaptive signal and image representation
Qubit
Mécanique quantique
Social networks
Aubry transition
Covariance
Adaptive transform
Unfolding
Amplification
Asymmetry
Clonage
Anomalous diffusio
2DRank algorithm
CheiRank algorithm
Quantum mechanics
Harper model
7215Rn
Matrix model
Information quantique
Algorithmes quantiques
Wikipedia networks
Beam splitter