Related papers: An uncertainty principle related to the Euclidean …

The assumption that an ensemble of classical particles is subject to nonclassical momentum fluctuations, with the fluctuation uncertainty fully determined by the position uncertainty, has been shown to lead from the classical equations of…

A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a…

New position uncertainty (delocalization) measures for a particle on the circle are proposed and illustrated on several examples, where the previous measures (based on 2pi-periodic position operators) appear to be unsatisfactory. The new…

In many areas of engineering and sciences, decision rules and control strategies are usually designed based on nominal values of relevant system parameters. To ensure that a control strategy or decision rule will work properly when the…

We shed new light on Heisenberg's uncertainty principle in the sense of Beurling, by offering an essentially different proof which permits us to weaken the assumptions substantially, and examples show that the result is sharp. The proof…

In this paper we give a discrete version of Hardy's uncertainty principle, by using complex variable arguments, as in the classical proof of Hardy's principle. Moreover, we give an interpretation of this principle in terms of decaying…

In the analysis of the on-axis intensity for a highly focused optical field it is highly desirable to deal with effective relations aimed at characterizing the field behavior in a rather simple fashion. Here, a novel and adequate measure…

This work shows that in the frame of the stochastic generalization of the quantum hydrodynamic analogy (QHA) the uncertainty principle can be derived by the postulate of finite transmission speed of light and information . The theory shows…

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…

In this article we discuss the question of presence of Hamiltonian cycle in the un-directed power graph of a group. In the process we develop weighted Hamiltonian cycle concept and prove a few general results regarding the Hamiltonian…

The uncertainty principle is considered to be one of the most striking features in quantum mechanics. In the textbook literature, uncertainty relations usually refer to the preparation uncertainty which imposes a limitation on the spread of…

It is shown that quasi all continuous functions on the unit circle have the property that, for many small subsets E of the circle, the partial sums of their Fourier series considered as functions restricted to E exhibit certain universality…

In this note, an alternative approach to establish observability for semigroups based on their smoothing properties is presented. The results discussed here are closely related to those recently obtained in [arXiv:2112.01788], but the…

We present a generalization of Hirschman's entropic uncertainty principle for locally compact abelian groups to unimodular locally compact quantum groups. As a corollary, we strengthen a well-known uncertainty principle for compact groups,…

The phenomenon in the essence of classical uncertainty principles is well known since the thirties of the last century. We introduce a new phenomenon which is in the essence of a new notion that we introduce: "Generalized Uncertainty…

Heisenberg's uncertainty principle implies fundamental constraints on what properties of a quantum system can we simultaneously learn. However, it typically assumes that we probe these properties via measurements at a single point in time.…

The aim of this paper is to establish a few uncertainty principles for the Fourier and the short-time Fourier transforms. Also, we discuss an analogue of Donoho--Stark uncertainty principle and provide some estimates for the size of the…

We provide a decision-theoretic framework for dealing with uncertainty in quantum mechanics. This uncertainty is two-fold: on the one hand there may be uncertainty about the state the quantum system is in, and on the other hand, as is…

Uncertainty quantification is essential when deploying learning-based control methods in safety-critical systems. This is commonly realized by constructing uncertainty tubes that enclose the unknown function of interest, e.g., the reward…

We study the uncertainty principles related to the generalized Logan problem in $\mathbb{R}^{d}$. Our main result provides the complete solution of the following problem: for a fixed $m\in \mathbb{Z}_{+}$, find \[ \sup\{|x|\colon…