Related papers: Excess of Fusion Frames: A Comprehensive Approach
We develop a cut finite element method (CutFEM) for convection-diffusion problems posed on mixed-dimensional domains, i.e., unions of manifolds of different dimensions arranged in a hierarchical structure where lower-dimensional components…
Partial tomography, which focuses on reconstructing reduced density matrices (RDMs), has emerged as a promising approach for characterizing complex quantum systems, particularly when full state tomography is impractical. Recently,…
We propose a scheme for translating metrological precision bounds into lower bounds on query complexity of quantum search algorithms. Within the scheme the link between quadratic performance enhancement in idealized quantum metrological and…
The current study aims to examine uncertainty relations for measurements from generalized equiangular tight frames. Informationally overcomplete measurements are a valuable tool in quantum information processing, including tomography and…
Computing modular coincidences can show whether a given substitution system, which is supported on a point lattice in R^d, consists of model sets or not. We prove the computatibility of this problem and determine an upper bound for the…
The study involves characterizations of dual pairs of frames which are optimal to handle erasures among all dual pairs for a finite dimensional Hilbert space. A new optimality measure using the Frobenius norm of the error operator has been…
The process of fusion of complex nuclei is of significant interest as an example of the collective nuclear motion of large amplitude as well as a route for synthesis of new superheavy chemical elements. This process is accompanied by the…
Recently, neural network for scene flow estimation show impressive results on automotive data such as the KITTI benchmark. However, despite of using sophisticated rigidity assumptions and parametrizations, such networks are typically…
Data erasure can often occur in communication. Guarding against erasures involves redundancy in data representation. Mathematically this may be achieved by redundancy through the use of frames. One way to measure the robustness of a frame…
We consider two conformal defects close to each other in a free theory, and study what happens as the distance between them goes to zero. This limit is the same as zooming out, and the two defects have fused to another defect. As we zoom in…
In this paper we discuss some topics related to the general theory of frames. In particular we focus our attention to the existence of different 'reconstruction formulas' for a given vector of a certain Hilbert space and to some refinement…
A method for the determination of absolute quantum detection efficiency is suggested based on the measurement of photocount statistics of twin beams. The measured histograms of joint signal-idler photocount statistics allow to eliminate an…
The concept of balancedly splittable orthogonal designs is introduced along with a recursive construction. As an application, equiangular tight frames over the real, complex, and quaternions meeting the Delsarte-Goethals-Seidel upper bound…
How well can multiple incompatible observables be implemented by a single measurement? This is a fundamental problem in quantum mechanics with wide implications for the performance optimization of numerous tasks in quantum information…
The combination of LiDAR and camera modalities is proven to be necessary and typical for 3D object detection according to recent studies. Existing fusion strategies tend to overly rely on the LiDAR modal in essence, which exploits the…
In sensing applications where multiple sensors observe the same scene, fusing sensor outputs can provide improved results. However, if some of the sensors are providing lower quality outputs, the fused results can be degraded. In this work,…
In this note we discuss subtleties associated with the efficiency corrections for measurements of off-diagonal cumulants and factorial moments for a situation when one deals with overlapping sets of particles, such as correlations between…
We develop the max-plus finite element method to solve finite horizon deterministic optimal control problems. This method, that we introduced in a previous work, relies on a max-plus variational formulation, and exploits the properties of…
Quantum metrology overcomes standard precision limits by exploiting collective quantum superpositions of physical systems used for sensing, with the prominent example of non-classical multiphoton states improving interferometric techniques.…
We introduce probabilistic frames to study finite frames whose elements are chosen at random. While finite tight frames generalize orthonormal bases by allowing redundancy, independent, uniformly distributed points on the sphere…