scholarly journals An asymptotic equipartition property for measures on model spaces

2018 ◽  
Vol 371 (2) ◽  
pp. 1379-1402
Author(s):  
Tim Austin
2021 ◽  
Vol 15 (1) ◽  
Author(s):  
Carlos Cabrelli ◽  
Ursula Molter ◽  
Daniel Suárez
Keyword(s):  

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
Darius Bunandar ◽  
Luke C. G. Govia ◽  
Hari Krovi ◽  
Dirk Englund

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.


2006 ◽  
Vol 949 ◽  
Author(s):  
Jeffrey P. Calame

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.


2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Tesfa Mengestie

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.


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

1982 ◽  
Vol 309 (1) ◽  
pp. 55-64 ◽  
Author(s):  
C. Jacquemin ◽  
G. Auger ◽  
C. Quesne

2020 ◽  
Vol 13 ◽  
pp. 283
Author(s):  
T. S. Kosmas ◽  
M. Kortelainen ◽  
J. Suhonen ◽  
J. Toivanen

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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