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