Quantum Wasserstein distances for quantum permutation groups
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_ | 1866915476361183232 |
|---|---|
| author | Anshu Jekel, David Landry, Therese Basa |
| author_facet | Anshu Jekel, David Landry, Therese Basa |
| contents | We seek an analog for the quantum permutation group $S_n^+$ of the normalized Hamming distance for permutations. We define three distances on the tracial state space of $C(S_n^+)$ that generalize the $L^1$-Wasserstein distance of probability measures on $S_n$ equipped with the normalized Hamming metric, for which we demonstrate basic metric properties, subadditivity under convolution, and density of the Lipschitz elements in the $\mathrm{C}^{\ast}$-algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_19269 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Wasserstein distances for quantum permutation groups Anshu Jekel, David Landry, Therese Basa Operator Algebras Primary: 46L67, 49Q22, Secondary: 46L89, 81R60 We seek an analog for the quantum permutation group $S_n^+$ of the normalized Hamming distance for permutations. We define three distances on the tracial state space of $C(S_n^+)$ that generalize the $L^1$-Wasserstein distance of probability measures on $S_n$ equipped with the normalized Hamming metric, for which we demonstrate basic metric properties, subadditivity under convolution, and density of the Lipschitz elements in the $\mathrm{C}^{\ast}$-algebra. |
| title | Quantum Wasserstein distances for quantum permutation groups |
| topic | Operator Algebras Primary: 46L67, 49Q22, Secondary: 46L89, 81R60 |
| url | https://arxiv.org/abs/2505.19269 |