A trace inequality arising from quantum information theory

被引：17

作者：

Fujii, JI ^{[1
]}

机构：

[1] Osaka Kyoiku Univ, Dept Arts & Sci Informat Sci, Osaka 5828582, Japan

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2005年 / 400卷

关键词：

trace inequality; Skew information; Jensen's inequality;

D O I：

10.1016/j.laa.2004.11.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a skew information of Lieb's type S-f,S-g (A, X) = Tr f(A)Xg(A)X - Tr f(A)g(A)X-2 for selfadjoint matrices A, X. We give conditions for f and g so that S-f,S-g is positive or negative. As another important application, we settle the problem posed by Yanagi, Furuichi and Kuriyama from quantum information theory. (c) 2004 Elsevier Inc. All rights reserved.

引用

页码：141 / 146

页数：6

共 9 条

[1]

Ando T, 2000, MATH INEQUAL APPL, V3, P307

[2]

Bhatia R., 2013, MATRIX ANAL

[3] Some inequalities for norms on matrices and operators [J].

Bourin, JC .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1999, 292 (1-3) :139-154

[4]

BOURIN JC, 2004, RGMIA MONOGRAPHS

[5]

FUJII JI, 2004, SURIKAISEKIKENKYUSHO, V1396, P85

[6]

FURUICHI S, 2003, INFORMATION, V6, P71

[7] Reliability function of general classical-quantum channel [J].

Holevo, AS .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2000, 46 (06) :2256-2261

[8] CONVEX TRACE FUNCTIONS AND WIGNER-YANASE-DYSON CONJECTURE [J].

LIEB, EH .

ADVANCES IN MATHEMATICS, 1973, 11 (03) :267-288

[9]

YANAGI K, LINEAR ALGEBRA APPL

← 1 →