Relating incompatibility, noncommutativity, ...
Document type :
Compte-rendu et recension critique d'ouvrage
DOI :
Title :
Relating incompatibility, noncommutativity, uncertainty and Kirkwood-Dirac nonclassicality
Author(s) :
De Bièvre, Stephan [Auteur]
Systèmes de particules et systèmes dynamiques [Paradyse]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Université de Lille
Systèmes de particules et systèmes dynamiques [Paradyse]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Université de Lille
Journal title :
Journal of Mathematical Physics
Pages :
022202
Publisher :
American Institute of Physics (AIP)
Publication date :
2023-02-01
ISSN :
0022-2488
HAL domain(s) :
Physique [physics]
Mathématiques [math]
Mathématiques [math]
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 >
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
Popular science :
Non
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