Characterizing the geometry of the Kirkwood-Dirac positive states

Langrenez, Christopher; Arvidsson-Shukur, David R. M.; De Bievre, Stephan

Type de document :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1063/5.0164672

Titre :

Characterizing the geometry of the Kirkwood-Dirac positive states

Auteur(s) :

Langrenez, Christopher [Auteur]
Systèmes de particules et systèmes dynamiques [Paradyse]
Université de Lille
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Arvidsson-Shukur, David R. M. [Auteur]
Hitachi Cambridge Laboratory [University of Cambridge]
De Bievre, Stephan [Auteur]

Université de Lille
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Systèmes de particules et systèmes dynamiques [Paradyse]

Titre de la revue :

Journal of Mathematical Physics

Éditeur :

American Institute of Physics (AIP)

Date de publication :

2024-07-10

ISSN :

0022-2488

Discipline(s) HAL :

Physique [physics]
Mathématiques [math]

Résumé en anglais : [en]

The Kirkwood-Dirac (KD) quasiprobability distribution can describe any quantum state with respect to the eigenbases of two observables $A$ and $B$. KD distributions behave similarly to classical joint probability distributions ...
Lire la suite >The Kirkwood-Dirac (KD) quasiprobability distribution can describe any quantum state with respect to the eigenbases of two observables $A$ and $B$. KD distributions behave similarly to classical joint probability distributions but can assume negative and nonreal values. In recent years, KD distributions have proven instrumental in mapping out nonclassical phenomena and quantum advantages. These quantum features have been connected to nonpositive entries of KD distributions. Consequently, it is important to understand the geometry of the KD-positive and -nonpositive states. Until now, there has been no thorough analysis of the KD positivity of mixed states. Here, we characterize how the full convex set of states with positive KD distributions depends on the eigenbases of $A$ and $B$. In particular, we identify three regimes where convex combinations of the eigenprojectors of $A$ and $B$ constitute the only KD-positive states: $(i)$ any system in dimension $2$; $(ii)$ an open and dense set of bases in dimension $3$; and $(iii)$ the discrete-Fourier-transform bases in prime dimension. Finally, we investigate if there can exist mixed KD-positive states that cannot be written as convex combinations of pure KD-positive states. We show that for some choices of observables $A$ and $B$ this phenomenon does indeed occur. We explicitly construct such states for a spin-$1$ system.Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Projet ANR :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Commentaire :

35 pages, 2 figures

Collections :