A NECESSARY AND SUFFICIENT CONDITION FOR POSITIVITY OF LINEAR MAPS ON M4 CONSTRUCTED FROM PERMUTATION PAIRS

被引：2
作者：
Zhao, Haili [1 ]
Hou, Jinchuan [1 ]
机构：
[1] Taiyuan Univ Technol, Coll Math, Taiyuan 030024, Peoples R China
来源：
OPERATORS AND MATRICES | 2015年 / 9卷 / 03期
关键词：
Matrix algebras; positive linear maps; permutations; inequalities;
D O I：
10.7153/oam-09-36
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A necessary and sufficient condition for a D-type map Phi(pi 1,pi 2) on 4x4 matrices constructed from a pair of arbitrary permutations {pi(1),pi(2)} to be positive is obtained.
引用
收藏
页码：597 / 617
页数：21
相关论文
共 16 条
  • [1] Alberti P., 1980, Rep. Math. Phys., V18, P163
  • [2] Augusiak R., 2011, J PHYS A, V44, P185
  • [3] On the existence of physical transformations between sets of quantum states
    Chefles, A
    Jozsa, R
    Winter, A
    [J]. INTERNATIONAL JOURNAL OF QUANTUM INFORMATION, 2004, 2 (01) : 11 - 21
  • [4] COMPLETELY POSITIVE LINEAR MAPS ON COMPLEX MATRICES
    CHOI, MD
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1975, 10 (03) : 285 - 290
  • [5] Spectral Conditions for Positive Maps
    Chruscinski, Dariusz
    Kossakowski, Andrzej
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2009, 290 (03) : 1051 - 1064
  • [6] Chuang I. N., 2000, Quantum Computation and Quantum Information
  • [7] Horn R.A., 2012, Matrix Analysis
  • [8] Hou J., 1998, Journal of Operator Theory, V39, P43
  • [9] Hou J. - C., 2010, J PHYS A, V43, P385
  • [10] A new criterion and a special class of k-positive maps
    Hou, Jinchuan
    Li, Chi-Kwong
    Poon, Yiu-Tung
    Qi, Xiaofei
    Sze, Nung-Sing
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 470 : 51 - 69
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