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Acta Mathematica Scientia

, Volume 39, Issue 1, pp 148–164 | Cite as

Positive Maps Constructed from Permutation Pairs

  • Jinchuan Hou (侯晋川)
  • Haili Zhao (赵海丽)
Article

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 \({\Phi _{{\pi _{1,}}{\pi _2}}}\) 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 {πp, πq} to have property (C) is given, where π is the permutation defined by π(i) = i + 1 mod n and 1 ≤ p < qn.

Key words

matrix algebras positive linear maps permutations quantum information 

2010 MR Subject Classification

15A86 47B49 47N50 

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Copyright information

© Wuhan Institutes of Physics and Mathematics, Chinese Academy of Sciences 2019

Authors and Affiliations

  • Jinchuan Hou (侯晋川)
    • 1
  • Haili Zhao (赵海丽)
    • 1
  1. 1.School of MathematicsTaiyuan University of TechnologyTaiyuanChina

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