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.
ASJC Scopus subject areas
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics