The high-dimension limit of characters of compact reductive Lie groups and restrictions on the production of quantum randomness
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913174557556736 |
|---|---|
| author | Borodako, Piotr Sawicki, Adam |
| author_facet | Borodako, Piotr Sawicki, Adam |
| contents | For any element $g$ of compact reductive group $G$ we investigate the asymptotic behavior of its normalized irreducible character in the high-dimension limit, $\frac{χ_λ(g)}{d_λ}$. We show that when $G$ is simple the limit vanishes besides identity element. For semisimple groups one gets the same results under the additional assumption that dimensions of irreducible representations of all simple components are going to infinity. Using the notion of approximate $t$-designs we connect this observations with bounds on the production of quantum randomness in large quantum systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_24553 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The high-dimension limit of characters of compact reductive Lie groups and restrictions on the production of quantum randomness Borodako, Piotr Sawicki, Adam Representation Theory Quantum Physics For any element $g$ of compact reductive group $G$ we investigate the asymptotic behavior of its normalized irreducible character in the high-dimension limit, $\frac{χ_λ(g)}{d_λ}$. We show that when $G$ is simple the limit vanishes besides identity element. For semisimple groups one gets the same results under the additional assumption that dimensions of irreducible representations of all simple components are going to infinity. Using the notion of approximate $t$-designs we connect this observations with bounds on the production of quantum randomness in large quantum systems. |
| title | The high-dimension limit of characters of compact reductive Lie groups and restrictions on the production of quantum randomness |
| topic | Representation Theory Quantum Physics |
| url | https://arxiv.org/abs/2510.24553 |