Related papers: Low coherence unit norm tight frames
Estimating the unitarity of an unknown quantum channel $\mathcal{E}$ provides information on how much it is unitary, which is a basic and important problem in quantum device certification and benchmarking. Unitarity estimation can be…
In this paper we demonstrate that there are distinct differences between real and complex equiangular tight frames (ETFs) with regards to erasures. For example, we prove that there exist arbitrarily large non-trivial complex equiangular…
In tensor completion, the latent nuclear norm is commonly used to induce low-rank structure, while substantially failing to capture the global information due to the utilization of unbalanced unfolding scheme. To overcome this drawback, a…
Robust fencing is an essential component of intermittently nonlinear filtering for mitigation of outlier interference. In such filtering, the upper and the lower fences establish a robust range that excludes noise outliers while including…
We show the optimal coherence of $2d$ lines in $\mathbb{C}^{d}$ is given by the Welch bound whenever a skew Hadamard of order $d+1$ exists. Our proof uses a variant of Hadamard doubling that converts any equiangular tight frame of size…
The union-find decoder is a leading algorithmic approach to the correction of quantum errors on the surface code, achieving code thresholds comparable to minimum-weight perfect matching (MWPM) with amortised computational time scaling…
Motivated by a host of recent applications requiring some amount of redundancy, frames are becoming a standard tool in the signal processing toolbox. In this paper, we study a specific class of frames, known as discrete Fourier transform…
The sparse signal processing literature often uses random sensing matrices to obtain performance guarantees. Unfortunately, in the real world, sensing matrices do not always come from random processes. It is therefore desirable to evaluate…
We consider estimating a random vector from its noisy projections onto low dimensional subspaces constituting a fusion frame. A fusion frame is a collection of subspaces, for which the sum of the projection operators onto the subspaces is…
Over-complete systems of vectors, or in short, frames, play the role of analog codes in many areas of communication and signal processing. To name a few, spreading sequences for code-division multiple access (CDMA), over-complete…
Aerospace design is increasingly incorporating Design Under Uncertainty based approaches to lead to more robust and reliable optimal designs. These approaches require dependable estimates of uncertainty in simulations for their success. The…
With the maturation of quantum computing technology, research has gradually shifted towards exploring its applications. Alongside the rise of artificial intelligence, various machine learning methods have been developed into quantum…
Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being…
The significance of multi-scale features has been gradually recognized by the edge detection community. However, the fusion of multi-scale features increases the complexity of the model, which is not friendly to practical application. In…
Current 3D geometric molecular representations predominantly focus on discrete atomic skeletons, inherently overlooking the continuous electron density (ED) field that fundamentally governs microscopic quantum behaviors. Consequently, these…
Vector sets with optimal coherence according to the Welch bound cannot exist for all pairs of dimension and cardinality. If such an optimal vector set exists, it is an equiangular tight frame and represents the solution to a Grassmannian…
The increasingly crowded radio frequency (RF) spectrum forces communication signals to coexist, creating heterogeneous interferers whose structure often departs from Gaussian models. Recovering the interference-contaminated signal of…
Given the importance of future large scale structure surveys for delivering new cosmological information, it is crucial to reliably predict their observables. The Effective Field Theory of Large Scale Structures (EFTofLSS) provides a…
The requirement of high spectrum efficiency puts forward higher requirements on frame synchronization (FS) in wireless communication systems. Meanwhile, a large number of nonlinear devices or blocks will inevitably cause nonlinear…
The $h$-version of the finite-element method ($h$-FEM) applied to the high-frequency Helmholtz equation has been a classic topic in numerical analysis since the 1990s. It is now rigorously understood that (using piecewise polynomials of…