Related papers: A quantum wavelet uncertainty principle
We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One…
We propose a rigorous framework for Uncertainty Quantification (UQ) in which the UQ objectives and the assumptions/information set are brought to the forefront. This framework, which we call \emph{Optimal Uncertainty Quantification} (OUQ),…
To more flexibly balance between exploration and exploitation, a new meta-heuristic method based on Uncertainty Principle concepts is proposed in this paper. UP is is proved effective in multiple branches of science. In the branch of…
The Generalized Uncertainty Principle and the related minimum length are normally considered in non-relativistic Quantum Mechanics. Extending it to relativistic theories is important for having a Lorentz invariant minimum length and for…
This review is designed to introduce mathematicians and computational scientists to quantum computing (QC) through the lens of uncertainty quantification (UQ) by presenting a mathematically rigorous and accessible narrative for…
The purpose of this short note is to exhibit a new connection between the Heisenberg Uncertainty Principle on the line and the Breitenberger Uncertainty Principle on the circle, by considering the commutator of the multiplication and…
In this paper, the generic uncertainty relation (UR) for kernel-based transformations (KT) of signals is derived. Instead of using the statistics approach as shown in the literature before, here we employ quantum mechanical operator…
In this paper we introduce a new localization framework for wavelet transforms, such as the 1D wavelet transform and the Shearlet transform. Our goal is to design nonadaptive window functions that promote sparsity in some sense. For that,…
Minimization of the expectation value of energy under the constraints imposed by the uncertainty principle can be a convenient method of solving quantum-mechanical problems.
We revisit the uncertainty principle from the point of view suggested by A. Wigderson and Y. Wigderson. This approach is based on a primary uncertainty principle from which one can derive several inequalities expressing the impossibility of…
A universal formulation of uncertainty relations for quantum measurements is presented with additional focus on the representability of quantum observables by classical observables over a given state. Owing to the simplicity and operational…
With a q-deformed quantum mechanical framework, features of the uncertainty relation and a novel formulation of the Schr\"odinger equation are considered.
We study analytically and numerically the effects of various imperfections in a quantum computation of a simple dynamical model based on the Quantum Wavelet Transform (QWT). The results for fidelity timescales, obtained for a large range of…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
In two articles, the authors claim that the Heisenberg uncertainty principle limits the precision of simultaneous measurements of the position and velocity of a particle and refer to experimental evidence that supports their claim. It is…
In this paper, we introduce a family of integral transforms, denoted by \(\mathcal{O}_{\alpha}\), and constructed via kernel fusion of the fractional Fourier transform (FRFT) with angle \(\alpha \notin \pi \mathbb{Z}\). We demonstrate that…
Heisenberg's uncertainty principle has been understood to set a limitation on measurements; however, the long-standing mathematical formulation established by Heisenberg, Kennard, and Robertson does not allow such an interpretation.…
The full algebra of relativistic quantum mechanics (Lorentz plus Heisenberg) is unstable. Stabilization by deformation leads to a new deformation parameter $\epsilon \ell ^{2}$, $\ell $ being a length and $\epsilon$ a $\pm$ sign. The…
We present a simple but general treatment of neutrino oscillations in the framework of quantum mechanics using plane waves and intuitive wave packet principles when necessary. We attempt to clarify some confusing statements that have…
In 1996 Chui and Wang proved that the uncertainty constants of scaling and wavelet functions tend to infinity as smoothness of the wavelets grows for a broad class of wavelets such as Daubechies wavelets and spline wavelets. We construct a…