The Kirkwood-Dirac representation associated to the Fourier transform for finite abelian groups: positivity
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912586713268224 |
|---|---|
| author | De Bièvre, Stephan Langrenez, Christopher Radchenko, Danylo |
| author_facet | De Bièvre, Stephan Langrenez, Christopher Radchenko, Danylo |
| contents | We construct and study the Kirkwood-Dirac (KD) representations naturally associated to the Fourier transform of finite abelian groups $G$. We identify all pure KD-positive states and all KD-real observables for these KD representations. We provide a necessary and sufficient condition ensuring that all KD-positive states are convex combinations of pure KD-positive states. We prove that for $G=\Z_{d}$, with $d$ a prime power, this condition is satisfied. We provide examples of abelian groups where it is not. In those cases, the convex set of KD-positive states contains states outside the convex hull of the pure KD-positive states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12252 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Kirkwood-Dirac representation associated to the Fourier transform for finite abelian groups: positivity De Bièvre, Stephan Langrenez, Christopher Radchenko, Danylo Quantum Physics Mathematical Physics We construct and study the Kirkwood-Dirac (KD) representations naturally associated to the Fourier transform of finite abelian groups $G$. We identify all pure KD-positive states and all KD-real observables for these KD representations. We provide a necessary and sufficient condition ensuring that all KD-positive states are convex combinations of pure KD-positive states. We prove that for $G=\Z_{d}$, with $d$ a prime power, this condition is satisfied. We provide examples of abelian groups where it is not. In those cases, the convex set of KD-positive states contains states outside the convex hull of the pure KD-positive states. |
| title | The Kirkwood-Dirac representation associated to the Fourier transform for finite abelian groups: positivity |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2501.12252 |