Relating incompatibility, noncommutativity, uncertainty and Kirkwood-Dirac nonclassicality

de Bievre, Stephan

Document type :

Pré-publication ou Document de travail

Link :

https://lilloa.univ-lille.fr/handle/20.500.12210/122358

Title :

Relating incompatibility, noncommutativity, uncertainty and Kirkwood-Dirac nonclassicality

Author(s) :

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

English keyword(s) :

information theory
quantum
noncommutative

HAL domain(s) :

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

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Submission date :

2025-01-24T15:48:31Z

Files

2207.07451
Open access
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