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arXiv:1211.0386

Criteria and new classes of k-positive maps

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

Published Nov 2, 2012• 6 citations
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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.
DOI
10.48550/arxiv.1211.0386

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In quantum information theory, measurements are represented by positive, operator-valued measures. In this paper, we use the operators corresponding to generalized equiangular measurements to construct positive maps. Their positivity follows from the properties of index of coincidence for few equiangular tight frames. These maps give rise to entanglement witnesses, which include as special cases many important classes considered in the literature. Additionally, we introduce separability criteria based on the correlation matrix and analyze them for various types of measurements.