ENTANGLEMENT WITNESSES CONSTRUCTED BY PERMUTATION PAIRS  

作　　者：Jinchuan HOU Wenli WANG 侯晋川;王文丽(School of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China)

机构地区：[1]School of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China

出　　处：《Acta Mathematica Scientia》2021年第3期843-874,共32页数学物理学报（B辑英文版）

基　　金：partially supported by National Natural Science Foundation of China(11671294,12071336)。

摘　　要：For n≥3,we construct a class{Wn,π1,π2}of n^(2)×n^(2) hermitian matrices by the permutation pairs and show that,for a pair{π1,π2}of permutations on(1,2,…,n),Wn,π1,π2 is an entanglement witness of the n⊗n system if{π1,π2}has the property(C).Recall that a pair{π1,π2}of permutations of(1,2,…,n)has the property(C)if,for each i,one can obtain a permutation of(1,…,i−1,i+1,…,n)from(π1(1),…,π1(i−1),π1(i+1),…,π1(n))and(π2(1),…,π2(i−1),π2(i+1),…,π2(n)).We further prove that Wn,π1,π2 is not comparable with Wn,π,which is the entanglement witness constructed from a single permutationπ;Wn,π1,π2 is decomposable ifπ1π2=id orπ21=π22=id.For the low dimensional cases n∈{3,4},we give a sufficient and necessary condition onπ1,π2 for Wn,π1,π2 to be an entanglement witness.We also show that,for n∈{3,4},Wn,π1,π2 is decomposable if and only ifπ1π2=id orπ21=π22=id;W3,π1,π2 is optimal if and only if(π1,π2)=(π,π2),whereπ=(2,3,1).As applications,some entanglement criteria for states and some decomposability criteria for positive maps are established.

关 键 词：Separable states entangled states positive maps entanglement witnesses PERMUTATIONS 

分 类 号：O413[理学—理论物理]