A new criterion and a special class of k-positive maps Dedicated to Professor Leiba Rodman

Jinchuan Hou, Chi Kwong Li, Yiu Tung Poon, Xiaofei Qi, Nung Sing Sze

Research output: Journal article publicationJournal articleAcademic researchpeer-review

11 Citations (Scopus)

Abstract

We study k-positive maps on operators. We obtain a new criterion on k-positivity in terms of the k-numerical range, and use it to improve and refine some earlier results on k-positive maps related to the study of quantum information science. We also consider a special class of positive maps extending the construction of Choi on positive maps that are not completely positive. Some open questions on the decomposability of such maps are answered.
Original languageEnglish
Pages (from-to)51-69
Number of pages19
JournalLinear Algebra and Its Applications
Volume470
DOIs
Publication statusPublished - 1 Apr 2015

Keywords

  • k-numericalrange
  • k-positivemaps

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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