相关论文: Uncertainty Principles for the Offset Linear Canon…

We develop a theory describing the effects of many-particle Coulomb correlations on the coherent ultrafast nonlinear optical response of semiconductors and metals. Our approach is based on a mapping of the nonlinear optical response of the…

One native source of quality deterioration in medical imaging, and especially in our case optical coherence tomography (OCT), is the turbid biological media in which photon does not take a predictable path and many scattering events would…

Previous Facial Beauty Prediction (FBP) methods generally model FB feature of an image as a point on the latent space, and learn a mapping from the point to a precise score. Although existing regression methods perform well on a single…

All-quantum signal processing techniques are at the core of the successful advancement of most information-based quantum technologies. This paper develops coherent and comprehensive methodologies and mathematical models to describe Fourier…

This paper introduces Uncertainty Propagation Network (UPN), a novel family of neural differential equations that naturally incorporate uncertainty quantification into continuous-time modeling. Unlike existing neural ODEs that predict only…

Linear-optical circuits are elementary building blocks for classical and quantum information processing with light. In particular, due to its monolithic structure, integrated photonics offers great phase-stability and can rely on the large…

Optical unitary converter (OUC) that can convert a set of N mutually orthogonal optical modes into another set of arbitrary N orthogonal modes is expected to be the key device in diverse applications, including the optical communication,…

We give an overview of linear optics quantum computing, focusing on the results from the original KLM paper. First we give a brief summary of the advances made with optics for quantum computation prior to KLM. We next discuss the KLM linear…

We consider asymptotic behavior of Fourier transforms of stationary ergodic sequences with finite second moments. We establish a central limit theorem (CLT) for almost all frequencies and also an annealed CLT. The theorems hold for all…

Inverse scattering in optical coherence tomography (OCT) seeks to recover both structural images and intrinsic tissue optical properties, including refractive index, scattering coefficient, and anisotropy. This inverse problem is…

In this paper, we define a new transform called the Gabor quaternionic Fourier transform (GQFT), which generalizes the classical windowed Fourier transform to quaternion valued-signals, we give several important properties such as the…

We show various uncertainty principles for the Fourier transform on harmonic manifolds of rank one. In particular, we derive a Heisenberg uncertainty principle, a Morgen theorem, an uncertainty principle for the Schr\"odinger equation and a…

The manipulation of the quantum states of light in linear optical systems has multiple applications in quantum optics and quantum computation. The package QOptCraft gives a collection of methods to solve some of the most usual problems when…

We show that in principle, $N$-partite unitary transformations can be perfectly discriminated under local measurement and classical communication (LOCC) despite of their nonlocal properties. Based on this result, some related topics,…

The graph linear canonical transform (GLCT) is presented as an extension of the graph Fourier transform (GFT) and the graph fractional Fourier transform (GFrFT), offering more flexibility as an effective tool for graph signal processing. In…

These lecture notes are devoted to selected topics related to the uncertainty principle in harmonic analysis. Rather than attempting a systematic treatment, we emphasize only a number of both classical and deep manifestations of this…

The Continuous Spontaneous Localization (CSL) model strives to describe the quantum-to-classical transition from the viewpoint of collapse models. However, its original formulation suffers from a fundamental inconsistency in that it is…

In this paper, we introduce a new nonlinear optical channel equalizer based on Transformers. By leveraging parallel computation and attending directly to the memory across a sequence of symbols, we show that Transformers can be used…

The Fourier Transform is one of the most important linear transformations used in science and engineering. Cooley and Tukey's Fast Fourier Transform (FFT) from 1964 is a method for computing this transformation in time $O(n\log n)$.…

We mostly survey results concerning the $L^2$ boundedness of oscillatory and Fourier integral operators. This article does not intend to give a broad overview; it mainly focusses on a few topics directly related to the work of the authors.