Related papers: Noncommutative Uncertainty Principles

By building on our earlier work, we establish uncertainty principles in terms of Heisenberg inequalities and of the ambiguity functions associated with magnetic structures on certain coadjoint orbits of infinite-dimensional Lie groups.…

We derive an uncertainty principle for Lipschitz maps acting on subsets of Banach spaces. We show that this nonlinear uncertainty principle reduces to the Heisenberg-Robertson-Schrodinger uncertainty principle for linear operators acting on…

Heisenberg's uncertainty principle states that the position and momentum of a particle cannot be sharply determined simultaneously. Standard-deviation and entropic formulations capture the spread of the probability distribution but say…

Let G be a finite abelian group of order n. For a complex valued function f on G, let \fht denote the Fourier transform of f. The uncertainty inequality asserts that if f \neq 0 then |supp(f)| |supp(\fht)| \geq n. Answering a question of…

An inequality refining the lower bound for a periodic (Breitenberger) uncertainty constant is proved for a wide class of functions. A connection of uncertainty constants for periodic and non-periodic functions is extended to this class. A…

Information-theory based variational principles have proven effective at providing scalable uncertainty quantification (i.e. robustness) bounds for quantities of interest in the presence of nonparametric model-form uncertainty. In this…

In this article, we prove various smooth uncertainty principles on von Neumann bi-algebras, which unify numbers of uncertainty principles on quantum symmetries, such as subfactors, and fusion bi-algebras etc, studied in quantum Fourier…

We obtain several versions of the Hausdorff-Young and Hardy-Littlewood inequalities for the $(k,a)$-generalized Fourier transform recently investigated at length by Ben Sa\"i d, Kobayashi, and {\O} rsted. We also obtain a number of weighted…

The uncertainty principle limits quantum states such that when one observable takes predictable values there must be some other mutually unbiased observables which take uniformly random values. We show that this restrictive condition plays…

In this paper we prove some uncertainty bounds for commutators and anti-commutators of observables in a $C^*$-algebra. We give a short, elementary proof of Robertson's Standard Uncertaity Principle in this setting. We also prove some other…

Let $\mathcal{E}$ be a Hilbert C*-module over a unital C*-algebra $\mathcal{A}$. Let $A: \mathcal{D}(A) \subseteq \mathcal{E} \to \mathcal{E}$ and $B: \mathcal{D}(B)\subseteq \mathcal{E}\to \mathcal{E}$ be possibly unbounded self-adjoint…

Let $G$ be a finite abelian group. If $f: G\rightarrow \bC$ is a nonzero function with Fourier transform $\hf$, the Donoho-Stark uncertainty principle states that $|\supp(f)||\supp(\hf)|\geq |G|$. The purpose of this paper is twofold.…

The classical Hausdorff-Young inequality for locally compact abelian groups states that, for $1\le p\le 2$, the $L^p$-norm of a function dominates the $L^q$-norm of its Fourier transform, where $1/p+1/q=1$. By using the theory of…

In this paper, we study a few versions of the uncertainty principle for the windowed Opdam--Cherednik transform. In particular, we establish the uncertainty principle for orthonormal sequences, Donoho--Stark's uncertainty principle,…

This paper studies the uncertainty principle for spherical $h$-harmonic expansions on the unit sphere of $\mathbb{R}^d$ associated with a weight function invariant under a general finite reflection group, which is in full analogy with the…

Breitenberger's uncertainty principle on the torus $\mathbb{T}$ and its higher-dimensional analogue on $\mathbb{S}^{d-1}$ are well understood. We give describe an entire family of uncertainty principles on compact manifolds $(M,g)$, which…

Let $G$ be a locally compact abelian group, and let $\widehat{G}$ denote its dual group, equipped with a Haar measure. A variant of the uncertainty principle states that for any $S \subset G$ and $\Sigma \subset \widehat{G}$, there exists a…

The purpose of this paper is to develop a Fourier uncertainty principle on compact Riemannian manifolds and contrast the underlying ideas with those arising in the setting of locally compact abelian groups. The key obstacle is the growth of…

For a family of weight functions $h_\kappa$ that are invariant under a reflection group, the uncertainty principle on the unit sphere in the form of $$ \min_{1 \le i \le d} \int_{\mathbb{S}^{d-1}} (1- x_i) |f(x)|^2 h_\kappa^2(x) d\sigma…

The aim of the paper is two-fold. First, we provide an explicit form of the functions for which equality holds for the uncertainty inequalities studied in \cite{Fei}. Second, we establish an $L^p$-type Heisenberg-Pauli-Weyl uncertainty…