Criteria and new classes of k-positive maps

Abstract

We study k-positive maps on operators. Proofs are given to different positivity criteria. Special attention is on positive maps arising in the study of quantum information science. Results of other researchers are extended and improved. New classes of positive maps are constructed. Some open questions are answered.

23 pages, revised title, added references and minor revision

References in corpus (2)

• Spectral conditions for positive maps
• Positive finite rank elementary operators and characterizing entanglement of states