Umegaki's relative entropy S(ω, φ) = Tr Dω(log Dω − log Dφ) (of states ω and φ with density operators Dω and Dφ, 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 Tr A log AB ≥ Tr A(log A + log B) is obtained for positive definite matrices A and B.
|Title of host publication||Asymptotic Theory of Quantum Statistical Inference: Selected Papers|
|Publisher||World Scientific Publishing Co.|
|Number of pages||21|
|ISBN (Print)||9789812563071, 9812560157, 9789812560155|
|Publication status||Published - Jan 1 2005|
ASJC Scopus subject areas
- Physics and Astronomy(all)