On the Bures metric, C*-norm, and the quantum metric
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866929381834752000 |
|---|---|
| author | Aguilar, Konrad Behera, Karina Omland, Tron Wu, Nicole |
| author_facet | Aguilar, Konrad Behera, Karina Omland, Tron Wu, Nicole |
| contents | We prove that the topology on the density space with respect to a unital C*-algebra and a faithful induced by the C*-norm is finer than the Bures metric topology. We also provide an example when this containment is strict. Next, we provide a metric on the density space induced by a quantum metric in the sense of Rieffel and prove that the induced topology is the same as the topology induced by the Bures metric and C*-norm when the C*-algebra is assumed to be finite dimensional. Finally, we provide an example of when the Bures metric and induced quantum metric are not metric equivalent. Thus, we provide a bridge between these aspects of quantum information theory and noncommutative metric geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07219 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Bures metric, C*-norm, and the quantum metric Aguilar, Konrad Behera, Karina Omland, Tron Wu, Nicole Operator Algebras Functional Analysis 46L89, 46L30, 58B34 We prove that the topology on the density space with respect to a unital C*-algebra and a faithful induced by the C*-norm is finer than the Bures metric topology. We also provide an example when this containment is strict. Next, we provide a metric on the density space induced by a quantum metric in the sense of Rieffel and prove that the induced topology is the same as the topology induced by the Bures metric and C*-norm when the C*-algebra is assumed to be finite dimensional. Finally, we provide an example of when the Bures metric and induced quantum metric are not metric equivalent. Thus, we provide a bridge between these aspects of quantum information theory and noncommutative metric geometry. |
| title | On the Bures metric, C*-norm, and the quantum metric |
| topic | Operator Algebras Functional Analysis 46L89, 46L30, 58B34 |
| url | https://arxiv.org/abs/2406.07219 |