Related papers: Uncertainty product for Vilenkin groups
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…
Generalized uncertainty principles are effective changes to the Heisenberg uncertainty principle that emerge in several quantum gravity models. In the present letter, we study the consequences that two classes of these modifications yield…
In this paper we study applications of U-bounds to coercive and isoperimetric problems for probability measures on finite and infinite products of H-type groups.
We analyze entropic uncertainty relations for two orthogonal measurements on a $N$-dimensional Hilbert space, performed in two generic bases. It is assumed that the unitary matrix $U$ relating both bases is distributed according to the Haar…
We introduce a new, reliable, and agnostic uncertainty measure for classification tasks called logit uncertainty. It is based on logit outputs of neural networks. We in particular show that this new uncertainty measure yields a superior…
We investigate the task of local marking for locally implementable unitary operations. In this setting, multipartite quantum unitary channels, chosen randomly from a known set, are distributed among spatially separated parties without…
Uncertainty Quantification (UQ) is essential for creating trustworthy machine learning models. Recent years have seen a steep rise in UQ methods that can flag suspicious examples, however, it is often unclear what exactly these methods…
We evaluate uncertainty quantification (UQ) methods for deep learning applied to liquid argon time projection chamber (LArTPC) physics analysis tasks. As deep learning applications enter widespread usage among physics data analysis, neural…
The $D$-dimensional harmonic system (i.e., a particle moving under the action of a quadratic potential) is, together with the hydrogenic system, the main prototype of the physics of multidimensional quantum systems. In this work we…
In recent years the discrepancy in the value of the Hubble parameter has been growing. Recently, there are works supporting the proposal that the uncertainty principles can solve the Hubble tension. Motivated by this proposal, we work with…
The classical uncertainty principles deal with functions on abelian groups. In this paper, we discuss the uncertainty principles for finite index subfactors which include the cases for finite groups and finite dimensional Kac algebras. We…
A refined notion of curvature for a linear system of Hermitian vector spaces, in the sense of Grothendieck, leads to the unitary classification of a large class of analytic Hilbert modules. Specifically, we study Hilbert sub-modules, for…
We define an inner product (suitably interpreted) on the K(n)-local spectrum LG := L_{K(n)}BG_+, where G is a finite group or groupoid. This gives an inner product on E^*BG_+ for suitable K(n)-local ring spectra E. We relate this to the…
We investigate the spectral properties of the product of $M$ complex non-Hermitian random matrices that are obtained by removing $L$ rows and columns of larger unitary random matrices uniformly distributed on the group ${\rm U}(N+L)$. Such…
Heisenberg's uncertainty principle, which imposes intrinsic restrictions on our ability to predict the outcomes of incompatible quantum measurements to arbitrary precision, demonstrates one of the key differences between classical and…
Despite the widespread adoption of large language models (LLMs) for recommendation, we demonstrate that LLMs often exhibit uncertainty in their recommendations. To ensure the trustworthy use of LLMs in generating recommendations, we…
Quantum uncertainty relations have deep-rooted significance on the formalism of quantum mechanics. Heisenberg's uncertainty relations attracted a renewed interest for its applications in quantum information science. Robertson derived a…
We study the time evolution of the reduced Wigner function for a class of quantum Brownian motion models. We derive two generalized uncertainty relations. The first consists of a sharp lower bound on the uncertainty function, $U = (\Delta…
The Generalized Uncertainty Principle arises from the Heisenberg Uncertainty Principle when gravity is taken into account, so the leading order correction to the standard formula is expected to be proportional to the gravitational constant…
We prove a new uncertainty principle for square-integrable irreducible unitary representations of connected Lie groups. The concentration of the matrix coefficients is measured in terms of weighted $L^p$ norms, with weights in the local…