THE PROPER FORMULA FOR RELATIVE ENTROPY AND ITS ASYMPTOTICS IN QUANTUM PROBABILITY

被引：333

作者：

HIAI, F ^{[1
]}

PETZ, D ^{[1
]}

机构：

[1] HUNGARIAN ACAD SCI, INST MATH, H-1364 BUDAPEST, HUNGARY

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 1991年 / 143卷 / 01期

关键词：

D O I：

10.1007/BF02100287

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Umegaki's relative entropy S(omega, phi) = Tr D-omega(log D-omega-log D-phi) (of states omega and phi with density operators D-omega and D-phi, 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 greater-than-or-equal-to Tr A(log A + log B) is obtained for positive definite matrices A and B.

引用

页码：99 / 114

页数：16

共 29 条

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