POSITIVE MAPS CONSTRUCTED FROM PERMUTATION PAIRS

doi:10.1007/s10473-019-0113-x

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (1): 148-164.doi: 10.1007/s10473-019-0113-x

POSITIVE MAPS CONSTRUCTED FROM PERMUTATION PAIRS

侯晋川, 赵海利

School of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China

收稿日期:2017-09-16 修回日期:2018-02-19 出版日期:2019-02-25 发布日期:2019-03-13
通讯作者: Jinchuan HOU E-mail:jinchuanhou@aliyun.com
作者简介:Haili ZHAO,zhaohaili927@aliyun.com
基金资助:
This work was partially supported by National Natural Science Foundation of China (11671294).

POSITIVE MAPS CONSTRUCTED FROM PERMUTATION PAIRS

Jinchuan HOU, Haili ZHAO

School of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China

Received:2017-09-16 Revised:2018-02-19 Online:2019-02-25 Published:2019-03-13
Contact: Jinchuan HOU E-mail:jinchuanhou@aliyun.com
Supported by:
This work was partially supported by National Natural Science Foundation of China (11671294).

摘要/Abstract

摘要： A property (C) for permutation pairs is introduced. It is shown that if a pair {π₁, π₂} of permutations of (1, 2, …, n) has property (C), then the D-type map Φ_{π₁, π₂} on n×n complex matrices constructed from {π₁, π₂} is positive. A necessary and sufficient condition is obtained for a pair {π₁, π₂} to have property (C), and an easily checked necessary and sufficient condition for the pairs of the form {π^p, π^q} to have property (C) is given, where π is the permutation defined by π(i)=i + 1 mod n and 1 ≤ p < q ≤ n.

关键词: matrix algebras, positive linear maps, permutations, quantum information

Abstract: A property (C) for permutation pairs is introduced. It is shown that if a pair {π₁, π₂} of permutations of (1, 2, …, n) has property (C), then the D-type map Φ_{π₁, π₂} on n×n complex matrices constructed from {π₁, π₂} is positive. A necessary and sufficient condition is obtained for a pair {π₁, π₂} to have property (C), and an easily checked necessary and sufficient condition for the pairs of the form {π^p, π^q} to have property (C) is given, where π is the permutation defined by π(i)=i + 1 mod n and 1 ≤ p < q ≤ n.

Key words: matrix algebras, positive linear maps, permutations, quantum information

侯晋川, 赵海利. POSITIVE MAPS CONSTRUCTED FROM PERMUTATION PAIRS[J]. 数学物理学报(英文版), 2019, 39(1): 148-164.

Jinchuan HOU, Haili ZHAO. POSITIVE MAPS CONSTRUCTED FROM PERMUTATION PAIRS[J]. Acta mathematica scientia,Series B, 2019, 39(1): 148-164.

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POSITIVE MAPS CONSTRUCTED FROM PERMUTATION PAIRS

POSITIVE MAPS CONSTRUCTED FROM PERMUTATION PAIRS

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