Log-majorization and matrix norm inequalities with application to quantum information
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910448959356928 |
|---|---|
| author | Hiai, Fumio |
| author_facet | Hiai, Fumio |
| contents | We are concerned with log-majorization for matrices in connection with the multivariate Golden--Thompson trace inequality and the Karcher mean (i.e., a multivariate extension of the weighted geometric mean). We show an extension of Araki's log-majorization and apply it to the $α$-$z$-Rényi divergence in quantum information. We discuss the equality cases in the multivariate trace inequality of Golden--Thompson type and in the norm inequality for the Karcher mean. The paper includes an appendix to correct the proof of the author's old result on the equality case in the norm inequality for the weighted geometric mean. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16067 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Log-majorization and matrix norm inequalities with application to quantum information Hiai, Fumio Functional Analysis Operator Algebras Quantum Physics 15A45, 47A64, 81P17 We are concerned with log-majorization for matrices in connection with the multivariate Golden--Thompson trace inequality and the Karcher mean (i.e., a multivariate extension of the weighted geometric mean). We show an extension of Araki's log-majorization and apply it to the $α$-$z$-Rényi divergence in quantum information. We discuss the equality cases in the multivariate trace inequality of Golden--Thompson type and in the norm inequality for the Karcher mean. The paper includes an appendix to correct the proof of the author's old result on the equality case in the norm inequality for the weighted geometric mean. |
| title | Log-majorization and matrix norm inequalities with application to quantum information |
| topic | Functional Analysis Operator Algebras Quantum Physics 15A45, 47A64, 81P17 |
| url | https://arxiv.org/abs/2402.16067 |