Related papers: Quadratic phase wave packet transform
Background: Windowed Fourier decompositions (WFD) are widely used in measuring stationary and non-stationary spectral phenomena and in describing pairwise relationships among multiple signals. Although a variety of WFDs see frequent…
For the power-law quantum wave packet in configuration space, the variance of the position observable may be divergent. Accordingly, the information-entropic formulation of the uncertainty principle becomes more appropriate than the…
The concepts of geometric phase and wave-particle duality are interlinked to several fundamental phenomena in quantum physics, but their mutual relationship still forms an uncharted open problem. Here we address this question by studying…
For matter wave scattering from passive quantum obstacles, we propose a phase diagram in terms of phase and modulus of scattering coefficients to explore all possible directional scattering patterns. In the phase diagram, we can not only…
Quantum signal processing (QSP) provides a representation of scalar polynomials of degree $d$ as products of matrices in $\mathrm{SU}(2)$, parameterized by $(d+1)$ real numbers known as phase factors. QSP is the mathematical foundation of…
Phase retrieval from phaseless short-time Fourier transform (STFT) measurements is known to be inherently unstable when measurements are taken with respect to a single window. While an explicit inversion formula exists, it is useless in…
Very recently the most general ensemble of qubits are identified using the notion of linearity; any of these qubits gets accepted by a Hadamard gate to generate the equal superposition of the qubit and its orthogonal. Towards more…
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer…
The Quantum Fourier transform (QFT) is a key ingredient in most quantum algorithms. We have compared various spin-based quantum computing schemes to implement the QFT from the point of view of their actual time-costs and the accuracy of the…
The special affine Fourier transform (SAFT) is a promising tool for analyzing non-stationary signals with more degrees of freedom. However, the SAFT fails in obtaining the local features of non-transient signals due to its global kernel and…
Quantum Signal Processing (QSP) is a technique that can be used to implement a polynomial transformation $P(x)$ applied to the eigenvalues of a unitary $U$, essentially implementing the operation $P(U)$, provided that $P$ satisfies some…
Quantum signal processing (QSP) and quantum singular value transformation (QSVT) are powerful techniques for the development of quantum procedures. They allow to derive circuits preparing desired polynomial transformations. Recent research…
Quantum information processing and its subfield, quantum image processing, are rapidly growing fields as a result of advancements in the practicality of quantum mechanics. In this paper, we propose a quantum algorithm for processing…
The vision of seamlessly integrating information transfer (IT) and microwave based power transfer (PT) in the same system has led to the emergence of a new research area, called wirelessly power communications (WPC). Extensive research has…
The Lorentz-invariant S-matrix elements in interacting quantum field theory (QFT) are used to represent the QFT state by a Lorentz-invariant many-time wave function. Such a wave function can be used to describe inelastic scattering…
Quantum state tomography is a central technique for the characterization and verification of quantum systems. Standard tomography is widely used for low-dimensional systems, but for larger systems, it becomes impractical due to the…
Quantum Phase Estimation (QPE) stands as a pivotal quantum computing subroutine that necessitates an inverse Quantum Fourier Transform (QFT). However, it is imperative to recognize that enhancing the precision of the estimation inevitably…
A compressive sensing (CS) reconstruction method for polynomial phase signals is proposed in this paper. It relies on the Polynomial Fourier transform, which is used to establish a relationship between the observation and sparsity domain.…
Many multi-dimensional signals appear in the real world, such as digital images and data that has spatial and temporal dimensions. How to show the spectrum of these multi-dimensional signals correctly is a key challenge in the field of…
We compare the behavior of a wave packet in the presence of a complex and a pure quaternionic potential step. This analysis, done for a gaussian convolution function, sheds new light on the possibility to recognize quaternionic deviations…