scholarly journals An asymptotic equipartition property for measures on model spaces

2018 ◽  
Vol 371 (2) ◽  
pp. 1379-1402
Author(s):  
Tim Austin
Keyword(s):  
Asymptotic Equipartition Property ◽  
Model Spaces

scholarly journals Multi-orbital Frames Through Model Spaces

2021 ◽  
Vol 15 (1) ◽  
Author(s):  
Carlos Cabrelli ◽  
Ursula Molter ◽  
Daniel Suárez
Keyword(s):  
Model Spaces

scholarly journals Numerical finite-key analysis of quantum key distribution

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
Darius Bunandar ◽  
Luke C. G. Govia ◽  
Hari Krovi ◽  
Dirk Englund
Keyword(s):  
Finite Number ◽  
Quantum Key Distribution ◽  
Key Distribution ◽  
Numerical Approach ◽  
Asymptotic Formulas ◽  
Quantum Computers ◽  
Secure Communications ◽  
Quantum Relative Entropy ◽  
Asymptotic Equipartition Property ◽  
Optimization Solvers

AbstractQuantum key distribution (QKD) allows for secure communications safe against attacks by quantum computers. QKD protocols are performed by sending a sizeable, but finite, number of quantum signals between the distant parties involved. Many QKD experiments, however, predict their achievable key rates using asymptotic formulas, which assume the transmission of an infinite number of signals, partly because QKD proofs with finite transmissions (and finite-key lengths) can be difficult. Here we develop a robust numerical approach for calculating the key rates for QKD protocols in the finite-key regime in terms of two semi-definite programs (SDPs). The first uses the relation between conditional smooth min-entropy and quantum relative entropy through the quantum asymptotic equipartition property, and the second uses the relation between the smooth min-entropy and quantum fidelity. The numerical programs are formulated under the assumption of collective attacks from the eavesdropper and can be promoted to withstand coherent attacks using the postselection technique. We then solve these SDPs using convex optimization solvers and obtain numerical calculations of finite-key rates for several protocols difficult to analyze analytically, such as BB84 with unequal detector efficiencies, B92, and twin-field QKD. Our numerical approach democratizes the composable security proofs for QKD protocols where the derived keys can be used as an input to another cryptosystem.

Microstructure-Based Simulation of the Dielectric Properties of Polymer-Ceramic Composites for Capacitor Applications

2006 ◽  
Vol 949 ◽  
Author(s):  
Jeffrey P. Calame
Keyword(s):  
Electric Field ◽  
Polymer Matrix ◽  
Matrix Material ◽  
Realistic Model ◽  
Ceramic Composites ◽  
Internal Electric Field ◽  
Large Particles ◽  
Different Types ◽  
Model Spaces ◽  
Electrostatic Modeling

ABSTRACTResearch on the microstructure-based modeling of composite dielectrics for capacitor applications is described. Methods for predicting the composite dielectric permittivity and internal electric field distributions within the microstructure using finite difference quasi-electrostatic modeling are described, along with methods of generating realistic model spaces of particulate microstructures. An existing algorithm for generating random, monosized spheres-in-a-dielectric matrix model spaces is modified to allow the treatment of bimodal composites in which small particles are deliberately segregated into the spaces between large particles. Such composites can have substantially higher total volumetric filling fractions of particles, leading to higher composite permittivity. The variations in permittivity with the filling fractions of bimodal inclusions are studied with the new model, with cases covering three different types of polymer matrix material. The effect of the small particle additions on the electric field statistics within the polymer matrix is also explored.

scholarly journals Volterra Type Integral Operators and Composition Operators on Model Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Tesfa Mengestie
Keyword(s):  
Composition Operators ◽  
Integral Operators ◽  
Volterra Type ◽  
Open Problems ◽  
Type Integral ◽  
Model Spaces

We study some mapping properties of Volterra type integral operators and composition operators on model spaces. We also discuss and give out a couple of interesting open problems in model spaces where any possible solution of the problems can be used to study a number of other operator theoretic related problems in the spaces.

Model Spaces for Compositions of Q - Functions

1998 ◽  
Vol 195 (1) ◽  
pp. 159-170 ◽  
Author(s):  
Michael Kaltenbäck
Keyword(s):  
Model Spaces

FixedJ spectral distributions in large shell model spaces

1982 ◽  
Vol 309 (1) ◽  
pp. 55-64 ◽  
Author(s):  
C. Jacquemin ◽  
G. Auger ◽  
C. Quesne
Keyword(s):  
Shell Model ◽  
Model Spaces ◽  
Large Shell ◽  
Spectral Distributions

scholarly journals Realistic Calculations for Cold Dark Matter Detection Rates

2020 ◽  
Vol 13 ◽  
pp. 283
Author(s):  
T. S. Kosmas ◽  
M. Kortelainen ◽  
J. Suhonen ◽  
J. Toivanen
Keyword(s):  
Dark Matter ◽  
Nuclear Structure ◽  
Large Scale ◽  
Cold Dark Matter ◽  
Scattering Problem ◽  
Realistic Model ◽  
Supersymmetric Particle ◽  
Detection Rates ◽  
Model Spaces ◽  
Event Rates

The scattering of the cold dark matter (CDM) candidate LSP (Lightest Supersymmetric Particle) off nuclei is investigated. We focus on the nuclear-structure aspects of the LSP-nucleus scattering problem and computed the associated event rates as well as the annual modulation signals for the 23Na, 71Ga, 73Ge and 127I CDM detectors by using the nuclear shell model in realistic model spaces and exploiting microscopic effective two-body interactions. Large-scale computations had to be performed in order to achieve convergence of the results. The relevance of the spin-dependent and coherent channels for the event rates is discussed, from both the nuclear structure and the SUSY-model viewpoints.

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