Related papers: An uncertainty principle for unimodular quantum gr…
We show that a compact quantum group all whose irreducible representations have dimension bounded by a fixed constant must be of Kac type, in other words, its Haar measure is a trace. The proof is based on establishing several facts…
Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be…
The uncertainty principle brings out intrinsic quantum bounds on the precision of measuring non-commuting observables. Statistical outcomes in the measurement of incompatible observables reveal a trade-off on the sum of corresponding…
We prove that amenability of a unitary co-representation $U$ of a locally compact quantum group passes to unitary co-representations that weakly contain $U$. This generalizes a result of Bekka, and answers affirmatively a question of…
A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements. Often the statistical uncertainties are…
In this article we deduce an analogue of Quillen's Local-Global Principle for the elementary subgroup of the general quadratic group and the hermitian group. We show that the unstable K_1-groups of the hermitian groups are nilpotent by…
The uncertainty principle sets limit on our ability to predict the values of two incompatible observables measured on a quantum particle simultaneously. This principle can be stated in various forms. In quantum information theory, it is…
We consider quantum algebras of observables associated with subregions in theories of Einstein gravity coupled to matter in the $G_N\rightarrow 0$ limit. When the subregion is spatially compact or encompasses an asymptotic boundary, we…
The Heisenberg uncertainty principle is known to be connected to the entropic uncertainty principle. This correspondence is obtained employing a Gaussian probability distribution for wave functions associated to the Shannon entropy.…
In the setting of von Neumann algebras, measurable quantum groupoids have successfully been axiomatized and studied by Enock, Vallin, and Lesieur, whereas in the setting of $C^{*}$-algebras, a similar theory of locally compact quantum…
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…
Heisenberg's uncertainty principle is formulated for a set of generalized measurements within the framework of majorization theory, resulting in a partial uncertainty order on probability vectors that is stronger than those based on…
In this note, we consider the implications of the Heisenberg uncertainty principle (HUP) when computing uncertainties that affect the main dynamical quantities, from the perspective of special relativity. Using the well-known formula for…
Let $\Gamma$ be a countable discrete group, $H$ a lcsc totally disconnected group and $\rho : \Gamma \rightarrow H$ a homomorphism with dense image. We develop a general and explicit technique which provides, for every compact open subgroup…
The uncertainty principle sets a bound on our ability to predict the measurement outcomes of two incompatible observables which are measured on a quantum particle simultaneously. In quantum information theory, the uncertainty principle can…
The uncertainty principle constitutes a fundamental pillar of quantum theory, representing one of the most distinctive features that differentiates quantum mechanics from classical physics. In this study, we firstly propose a novel…
Generalized uncertainty principles are able to serve as useful descriptions of some of the phenomenology of quantum gravity effects, providing an intuitive grasp on non-trivial space-time structures such as a fundamental discreteness of…
Two of the most intriguing features of quantum physics are the uncertainty principle and the occurrence of nonlocal correlations. The uncertainty principle states that there exist pairs of incompatible measurements on quantum systems such…
Entropic uncertainty relations provide an information-theoretic framework for quantifying the fundamental indeterminacy inherent in quantum mechanics. We propose more stringent quantum-memory-assisted entropic uncertainty relations for…
Let $\mathbb{H}\trianglelefteq\mathbb{G}$ be a closed normal subgroup of a locally compact quantum group. We introduce a strictly positive group-like element affiliated with $L^{\infty}(\mathbb{G})$ that, roughly, measures the failure of…