Related papers: Uncertainty principles on $C^{*}$-algebras

C*-algebras are rings, sometimes nonunital, obeying certain axioms that ensure a very well-behaved representation theory upon Hilbert space. Moreover, there are some well-known features of the representation theory leading to subtle…

We first present a generalization of the Robertson-Heisenberg uncertainty principle. This generalization applies to mixed states and contains a covariance term. For faithful states, we characterize when the uncertainty inequality is an…

Khosravi, Drnov\v{s}ek and Moslehian [\textit{Filomat, 2012}] derived Buzano inequality for Hilbert C*-modules. Using this inequality we derive Deutsch entropic uncertainty principle for Hilbert C*-modules over commutative unital…

The uncertainty relation is a distinguishing feature of quantum theory, characterizing the incompatibility of noncommuting observables in the preparation of quantum states. Recently, many uncertainty relations were proposed with improved…

Calling the quantity; 2delta(A)delta(B)/|<[A, B]>|, with non-zero denominator, the uncertainty product ratio or UPR for the pair of observables, (A, B), it is shown that any non-zero correlation coefficient between two observables raises,…

Motivated by a question of L. Robert, asking whether $\rm L(T(A)) = Lsc_{C}(T(A))$ for any separable C*-algebra A, we introduce and initiate the study of \emph{tracially reflexive C*-algebras}. We first prove that commutative C*-algebras…

The Ehrenfest theorem and the Robertson uncertainty relation are well-known basic equations in quantum mechanics. However, there exist problematic cases, where the Ehrenfest theorem and the Robertson uncertainty relation are not correct.…

In this paper, we show how the Robertson uncertainty relation gives certain intrinsic quantum limits of measurements in the most general and rigorous mathematical treatment. A general lower bound for the product of the root-mean-square…

The purpose of this note is to show that the construction of the C*-algebra for the space-time uncertainty relations which was introduced by Doplicher, Fredenhagen and Roberts fits comfortably into the strict deformation quantization…

The Basic Universal Deformation Formula is proven and applied to show that Weyl algebras, which encode Heisenberg's uncertainty principle, are effective deformations of polynomial rings, and that uncertainty is necessary for stability.…

Hilbert C*-modules are the analogues of Hilbert spaces where a C*-algebra plays the role of the scalar field. With the advent of Kasparov's celebrated KK-theory they became a standard tool in the theory of operator algebras. While the…

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…

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…

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…

We utilize quantum superposition principle to establish the improvable upper and lower bounds on the stronger uncertainty relation, i.e., the "weighted-like" sum of the variances of observables. Our bounds include some free parameters which…

We construct a C*-algebra that has only one irreducible representation up to unitary equivalence but is not isomorphic to the algebra of compact operators on any Hilbert space. This answers an old question of Naimark. Our construction uses…

We define a C*-hull for a *-algebra, given a notion of integrability for its representations on Hilbert modules. We establish a local-global principle which, in many cases, characterises integrable representations on Hilbert modules through…

The main purpose of this paper is to construct *-representations from unbounded C$^*$-seminorms on partial *-algebras and to investigate their *-representations.

The Heisenberg-Robertson uncertainty relation quantitatively expresses the impossibility of jointly sharp preparation of incompatible observables. However it does not capture the concept of incompatible observables because it can be trivial…

Entropic uncertainty relations place nontrivial lower bounds to the sum of Shannon information entropies for noncommuting observables. Here we obtain a novel lower bound on the entropy sum for general pairs of observables in…