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.

arXiv comment23 pages, revised title, added references and minor revision

References in corpus (6)

• Spectral conditions for positive maps
• How to construct entanglement witnesses
• Positive finite rank elementary operators and characterizing entanglement of states
• Physical transformations between quantum states
• Extremal extensions of entanglement witnesses: Unearthing new bound entangled states
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Cited by in corpus (3)

• Entanglement witnesses: construction, analysis and classification
• Random and free positive maps with applications to entanglement detection
• A class of generalized positive linear maps on matrix algebras