一对置换构造的4阶矩阵正线性映射

赵海利; 侯晋川

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一对置换构造的4阶矩阵正线性映射

更新时间：2026-09-14

- 一对置换构造的4阶矩阵正线性映射
- 一对置换构造的4阶矩阵正线性映射
- Issue 5, (2013)
- 作者机构：
  
  太原理工大学数学学院
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2013
- 稿件说明：
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赵海利, 侯晋川. 一对置换构造的4阶矩阵正线性映射[J]. 2013, (5).
DOI：

赵海利, 侯晋川. 一对置换构造的4阶矩阵正线性映射[J]. 2013, (5). DOI：

摘要

研究了4×4矩阵代数上

由一对置换{π1

π2}构造的D-type映射Φπ1

π2是正线性映射的条件.对(1

4)上的一对置换{π1

π2}引入性质(C)的概念

得到{π1

π2}具有性质(C)的充分必要条件.利用两个引理进而证明了如果{π1

π2}具有性质(C)

则由{π1

π2}构造的D-type映射Φπ1

π2在4×4矩阵代数上是正线性映射.依此可以构造新的正线性映射并应用于44复合量子系统量子纠缠性的检测.

Abstract

The conditions of positive D-type map Φπ1

π2constructed from a pair of permutations{π1

π2}on 4×4 matrix algebras was investigated.For a permutation pair{π1

π2}of(1

a notion of property(C)was introduced.A necessary and sufficient condition for{π1

π2}with the property(C)was obtained. Applying two lemmas

it is shown that

if{π1

π2}has the property(C)

then theD-type map Φπ1

π2 on 4× 4 matrix algebras constructed from{π1

π2}is positive

which proposes a new method to construct positive maps and may be applied to detect the entanglement in the quantum states of 44 composite systems.

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太原理工大学数学系

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