The proper formula for relative entropy and its asymptotics in quantum probability |
| |
Authors: | Fumio Hiai Dénes Petz |
| |
Institution: | (1) Department of Mathematics, Ibaraki University, 310 Mito, Ibaraki, Japan;(2) Mathematical Institute, Hungarian Academy of Sciences, P.O. Box 127, H-1364 Budapest, Hungary |
| |
Abstract: | Umegaki's relative entropyS(,)=TrD
(logD
–logD
) (of states and with density operatorsD
andD
, respectively) is shown to be an asymptotic exponent considered from the quantum hypothesis testing viewpoint. It is also proved that some other versions of the relative entropy give rise to the same asymptotics as Umegaki's one. As a byproduct, the inequality TrA logAB TrA(logA+logB) is obtained for positive definite matricesA andB. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|