Related papers: Uncertainty product for Vilenkin groups
Within the framework of quantum harmonic analysis, for a locally compact group $G$ with a square-integrable, irreducible unitary representation, we analyze the eigenvalue distributions of convolutions between indicator functions on $G$ and…
We report new results and generalizations of our work on unextendible product bases (UPB), uncompletable product bases and bound entanglement. We present a new construction for bound entangled states based on product bases which are only…
Classes of locally compact groups having qualitative uncertainty principle for Gabor transform have been investigated. These include Moore groups, Heisenberg Group $\mathbb{H}_n, \mathbb{H}_{n} \times D,$ where $D$ is discrete group and…
We establish the comparison principle, existence and regularity of viscosity solutions to the following problem concerning the mixed operator: \begin{align} \begin{cases}…
We provide formulas for invariants defined on a tensor product of defining representations of unitary groups, under the action of the product group. This situation has a physical interpretation, as it is related to the quantum mechanical…
We use deformation-rigidity theory in von Neumann algebra framework to study probability measure preserving actions by wreath product groups. In particular, we single out large families of wreath products groups satisfying various type of…
Incompatible observables can be approximated by compatible observables in joint measurement or measured sequentially, with constrained accuracy as implied by Heisenberg's original formulation of the uncertainty principle. Recently, Busch,…
The knapsack problem for groups was introduced by Miasnikov, Nikolaev, and Ushakov. It is defined for each finitely generated group $G$ and takes as input group elements $g_1,\ldots,g_n,g\in G$ and asks whether there are $x_1,\ldots,x_n\ge…
We study quantum corrections to the $\Lambda$CDM model model arising from a minimum measurable length in Heisenberg's uncertainty principle. We focus on a higher-order Generalized Uncertainty Principle, beyond the quadratic form. This…
Heisenberg's uncertainty principle, coherence and Bell nonlocality have been individually examined through many experiments. In this Letter, we systematically characterize all of this quantumness in a unified manner. We first construct…
We analyze the weak and critical points of various uncertainty relations that follow from the inequalities for the norms of vectors in the Hilbert space of states of a quantum system. There are studied uncertainty relations for sums of…
In the Copenhagen interpretation the Heisenberg uncertainty relation is interpreted as the mathematical expression of the concept of complementarity, quantifying the mutual disturbance necessarily taking place in a simultaneous or joint…
It has been recently shown that the Bekenstein entropy bound is not respected by the systems satisfying modified forms of Heisenberg uncertainty principle (HUP) including the generalized and extended uncertainty principles, or even their…
Supramenability of groups is characterised in terms of invariant measures on locally compact spaces. This opens the door to constructing interesting crossed product C*-algebras for non-supramenable groups. In particular, stable Kirchberg…
Uncertainty quantification, once a singular task, has evolved into a spectrum of tasks, including abstained prediction, out-of-distribution detection, and aleatoric uncertainty quantification. The latest goal is disentanglement: the…
In this article, we prove that if the Fourier transform of a certain integrable function on the Euclidean motion group is of finite rank, then the function has to vanish identically. Further, we explore a new variance of the uncertainty…
Following a general method proposed earlier, we construct here Wigner functions defined on coadjoint orbits of a class of semidirect product groups. The groups in question are such that their unitary duals consist purely of representations…
Heisenberg's uncertainty principle forms a fundamental element of quantum mechanics. Uncertainty relations in terms of entropies were initially proposed to deal with conceptual shortcomings in the original formulation of the uncertainty…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
We revisit considerations of temporal order in relativistic effects, taking into account Heisenberg's Uncertainty Principle. We then use a formulation of relativistic Quantum Mechanical equations given by Feshbach and Villars to exhibit…