Relating incompatibility, noncommutativity, uncertainty and Kirkwood-Dirac nonclassicality

de Bievre, Stephan

Type de document :

Pré-publication ou Document de travail

URL permanente :

http://hdl.handle.net/20.500.12210/122358

Titre :

Relating incompatibility, noncommutativity, uncertainty and Kirkwood-Dirac nonclassicality

Auteur(s) :

de Bievre, Stephan [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Mot(s)-clé(s) en anglais :

information theory
quantum
noncommutative

Discipline(s) HAL :

Physique [physics]/Physique Quantique [quant-ph]

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

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Date de dépôt :

2025-01-24T15:48:31Z

Fichiers

2207.07451
Accès libre
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