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We introduce a purely geometric formulation for two different measures addressed to quantify the entanglement between different parts of a tripartite qubit system. Our approach considers the entanglement-polytope defined by the smallest…

Quantum Physics · Physics 2024-10-29 Salvio Luna-Hernandez , Marco Enriquez , Oscar Rosas-Ortiz

The inverse scattering problems have been popular for the past thirty years. While very successful in many cases, progress has lagged when only {\em limited-aperture} measurement is available. In this paper, we perform some elementary study…

Numerical Analysis · Mathematics 2018-01-09 Xiaodong Liu , Jiguang Sun

We present a comprehensive mathematical study of the Magneto-Telluric (MT) method, on bounded domain in $\mathbb{R}^3$. We show that electrical conductivity and magnetic permeability, assumed to be $C^2$, can be uniquely recovered from MT…

Analysis of PDEs · Mathematics 2020-12-02 Yernat M. Assylbekov , Maarten V. de Hoop

The aim of this paper is to provide a fast and efficient procedure for (real-time) target identification in imaging based on matching on a dictionary of precomputed generalized polarization tensors (GPTs). The approach is based on some…

Optimization and Control · Mathematics 2013-02-27 Habib Ammari , Thomas Boulier , Josselin Garnier , Wenjia Jing , Hyœnbæ Kang , Han Wang

In the past decade, several neutron reflectometry methods for determining the modulus and phase of the complex reflection coefficient of an unknown multilayer thin film have been worked out among which the method of variation of…

Materials Science · Physics 2012-09-06 Seyed Farhad Masoudi , Saeed S. Jahromi

We are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-field measurement. Using the intrinsic geometric properties…

Analysis of PDEs · Mathematics 2017-06-15 Jingzhi Li , Xiaofei Li , Hongyu Liu

In recent years, structured matrix recovery problems have gained considerable attention for its real world applications, such as recommender systems and computer vision. Much of the existing work has focused on matrices with low-rank…

Machine Learning · Statistics 2016-04-13 Sheng Chen , Arindam Banerjee

We are concerned with the inverse scattering problem of recovering an inhomogeneous medium by the associated acoustic wave measurement. We prove that under certain assumptions, a single far-field pattern determines the values of a…

Analysis of PDEs · Mathematics 2020-05-05 Emilia Blåsten , Hongyu Liu

We describe a method for reconstructing multi-scale entangled states from a small number of efficiently-implementable measurements and fast post-processing. The method only requires single particle measurements and the total number of…

Quantum Physics · Physics 2014-12-02 Olivier Landon-Cardinal , David Poulin

We formulate a new conceptual approach for one-shot complete polarization state measurement with nanostructured metasurfaces applicable to classical light and multi-photon quantum states, by drawing on the principles of generalized quantum…

A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…

Numerical Analysis · Mathematics 2026-04-02 Jeffrey Uhlmann

We provide an explicit construction of quasi-invariant measures on polarized coadjoint orbits of a Lie group G. The use of specific (trivial) central extensions of G by the multiplicative group ${R}^+$ allows us to restore the strict…

Mathematical Physics · Physics 2015-06-26 J. Guerrero , V. Aldaya

Mueller matrices provide a complete description of a medium's response to excitation by polarized light, and their characterization is important across a broad range of applications from ellipsometry in material science to polarimetry in…

In this paper we study an inverse problem in convex geometry, inspired by a problem in materials science. Firstly, we consider the question of whether a Laguerre tessellation (a partition by convex polytopes) can be recovered from only the…

Optimization and Control · Mathematics 2025-01-22 David P. Bourne , Mason Pearce , Steven M. Roper

We present calculations that reconstruct electronic current densities in two stacked layers at known depths, using magnetic field data. Solving this inverse problem requires knowledge of the magnetic field in two planes -- one above both…

Obtaining conductance spectra for a concentration of disordered impurities distributed over a nanoscale device with sensing capabilities is a well-defined problem. However, to do this inversely, i.e., extracting information about the…

Mesoscale and Nanoscale Physics · Physics 2021-12-01 S. Mukim , J. O'Brien , M. Abarashi , M. S. Ferreira , C. G. Rocha

This paper is concerned with polarimetric dense map reconstruction based on a polarization camera with the help of relative depth information as a prior. In general, polarization imaging is able to reveal information about surface normal…

Computer Vision and Pattern Recognition · Computer Science 2021-02-11 Moein Shakeri , Shing Yan Loo , Hong Zhang

We consider the multi-channel inverse scattering problem in one-dimension in the presence of thresholds and bound states for a potential of finite support. Utilizing the Levin representation, we derive the general Marchenko integral…

Quantum Physics · Physics 2009-11-10 M. Braun , S. A. Sofianos , H. Leeb

The vectorial structure of light, amplitude, phase, and polarization, encodes essential information for applications ranging from super-resolution microscopy to high-capacity communications and quantum information processing. However,…

In this work, we propose a generalized multiscale inversion algorithm for heterogeneous problems that aims at solving an inverse problem on a computational coarse grid. Previous inversion techniques for multiscale problems seek a…

Numerical Analysis · Mathematics 2017-07-27 Eric T. Chung , Yalchin Efendiev , Bangti Jin , Wing Tat Leung , Maria Vasilyeva