Constructing positive maps from block matrices

TL;DR

This paper explores the relationship between positive block matrices and quantum positive maps, introducing new methods to construct both decomposable and non-completely positive maps for entanglement detection.

Contribution

It provides novel techniques for constructing positive maps from block matrices, enhancing tools for quantum entanglement detection.

Findings

Derived a method for constructing decomposable maps from positive block matrices.

Established a way to create positive but not completely positive maps from Hermitian block matrices.

Characterized the relation between positive block matrices and completely positive trace-preserving maps.

Abstract

Positive maps are useful for detecting entanglement in quantum information theory. Any entangled state can be detected by some positive map. In this paper, the relation between positive block matrices and completely positive trace-preserving maps is characterized. Consequently, a new method for constructing decomposable maps from positive block matrices is derived. In addition, a method for constructing positive but not completely positive maps from Hermitian block matrices is also obtained.