Lieb's simple proof of concavity of Tr A^p K^* B^(1-p) K and remarks on related inequalities
| dc.creator | Ruskai, Mary Beth | |
| dc.date | 2004-04-21 | |
| dc.date | 2006-04-27 | |
| dc.date.accessioned | 2026-07-07T12:29:18Z | |
| dc.date.available | 2026-07-07T12:29:18Z | |
| dc.description | A simple, self-contained proof is presented for the concavity of the map (A,B) --> Tr(A^p K^* B^(1-p) K). The author makes no claim to originality; this note gives Lieb's original argument in its simplest, rather than its most general, form. A sketch of the chain of implications from this result to concavity of A --> Tr e^[K + log(A)] is then presented. An independent elementary proof is given for the joint convexity of the map (A,B,X) --> Tr \int X^* (A+ uI)^{-1} X (B+ uI)^{-1} du which plays a key role in entropy inequalities. | |
| dc.description | Version 3 contains Appendix C, which corrects some flaws in the presentation of the proof of the main theorem | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0404126 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0404126 | |
| dc.identifier | International Jour. Quant. Info 3, 570--590 (2005); erratum 4, 747-748 (2006) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/215832 | |
| dc.subject | Quantum Physics | |
| dc.subject | Mathematical Physics | |
| dc.subject | Rings and Algebras | |
| dc.title | Lieb's simple proof of concavity of Tr A^p K^* B^(1-p) K and remarks on related inequalities | |
| dc.type | text |