DECOMPOSITION AND PARTIAL TRACE OF POSITIVE MATRICES WITH HERMITIAN BLOCKS

被引：12

作者：

Bourin, J-C. ^{[1
]}

Lee, Eun-Young ^{[2
]}

机构：

[1] Univ Franche Comte, Math Lab, F-25000 Besancon, France

[2] Kyungpook Natl Univ, Dept Math, Taegu 702701, South Korea

来源：

INTERNATIONAL JOURNAL OF MATHEMATICS | 2013年 / 24卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

Positive definite matrices; norm inequalities; partial trace; separable state; STATES;

D O I：

10.1142/S0129167X13500109

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let H = [A(s, t)] be a positive definite matrix written in beta x beta Hermitian blocks and let Delta = A(1,1) + ... + A(beta, beta) be its partial trace. Assume that beta = 2(p) for some p is an element of N. Then, up to a direct sum operation, H is the average of beta matrices isometrically congruent to Delta. A few corollaries are given, related to important inequalities in quantum information theory such as the Nielsen-Kempe separability criterion.

引用

页数：13

共 50 条

[1] POSITIVE DEFINITE COMPLETIONS OF PARTIAL HERMITIAN MATRICES
GRONE, R
JOHNSON, CR
SA, EM
WOLKOWICZ, H
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1984, 58 (APR) : 109 - 124
[2] POSITIVE SEMIDEFINITE COMPLETIONS OF PARTIAL HERMITIAN MATRICES
DANCIS, J
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1992, 175 : 97 - 114
[3] Positive matrices partitioned into a small number of Hermitian blocks
Bourin, Jean-Christophe
Lee, Eun-Young
Lin, Minghua
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2013, 438 (05) : 2591 - 2598
[4] On some trace inequalities for positive definite Hermitian matrices
Houqing Zhou
[J]. Journal of Inequalities and Applications, 2014
[5] On some trace inequalities for positive definite Hermitian matrices
Zhou, Houqing
[J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2014,
[6] Hermitian matrices and the trace of sub-Hermitian matrices
Liu, Yu
[J]. PROCEEDINGS OF THE THIRD INTERNATIONAL WORKSHOP ON MATRIX ANALYSIS AND APPLICATIONS, VOL 3, 2009, : 126 - 131
[7] Partial trace inequalities for partial transpose of positive semidefinite block matrices
Yang, Junjian
Xu, Huan
[J]. POSITIVITY, 2024, 28 (02)
[8] Partial trace inequalities for partial transpose of positive semidefinite block matrices
Junjian Yang
Huan Xu
[J]. Positivity, 2024, 28
[9] POSITIVE DEFINITE HERMITIAN MATRICES
KIRBY, D
[J]. MATRIX AND TENSOR QUARTERLY, 1972, 23 (01): : 31 - &
[10] A FACTORIZATION OF POSITIVE HERMITIAN MATRICES
WIENER, N
AKUTOWICZ, EJ
[J]. JOURNAL OF MATHEMATICS AND MECHANICS, 1959, 8 (01): : 111 - 120

← 1 2 3 4 5 →