Relating incompatibility, noncommutativity, uncertainty and Kirkwood-Dirac nonclassicality

De Bièvre, Stephan

Type de document :

Article dans une revue scientifique: Article original

DOI :

10.1063/5.0110267

Titre :

Relating incompatibility, noncommutativity, uncertainty and Kirkwood-Dirac nonclassicality

Auteur(s) :

De Bièvre, Stephan [Auteur]
Systèmes de particules et systèmes dynamiques [Paradyse]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Université de Lille

Titre de la revue :

Journal of Mathematical Physics

Pagination :

022202

Éditeur :

American Institute of Physics (AIP)

Date de publication :

2023-02-01

ISSN :

0022-2488

Discipline(s) HAL :

Physique [physics]
Mathématiques [math]

Résumé en anglais : [en]

We provide an in-depth study of the recently introduced notion of completely incompatible observables and its links to the support uncertainty and to the Kirkwood-Dirac nonclassicality of pure quantum states. The latter ...
Lire la suite >We provide an in-depth study of the recently introduced notion of completely incompatible observables and its links to the support uncertainty and to the Kirkwood-Dirac nonclassicality of pure quantum states. The latter notion has recently been proven central to a number of issues in quantum information theory and quantum metrology. In this last context, it was shown that a quantum advantage requires the use of Kirkwood-Dirac nonclassical states. We establish sharp bounds of very general validity that imply that the support uncertainty is an efficient Kirkwood-Dirac nonclassicality witness. When adapted to completely incompatible observables that are close to mutually unbiased ones, this bound allows us to fully characterize the Kirkwood-Dirac classical states as the eigenvectors of the two observables. We show furthermore that complete incompatibility implies several weaker notions of incompatibility, among which features a strong form of noncommutativity.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Projet ANR :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :