A general scheme for construction of scalar separability criteria from positive maps

TL;DR

This paper introduces a universal method to derive scalar separability criteria from positive maps, enhancing the detection of entanglement, including bound entanglement, beyond existing entropic inequalities.

Contribution

It proposes a novel scheme to construct scalar criteria from positive maps by decomposing them into completely positive parts, generalizing entropic inequalities and improving entanglement detection.

Findings

New scalar criteria outperform entropic inequalities

Criteria can detect bound entanglement

Applicable to various classes of quantum states

Abstract

We present a general scheme that allows for construction of scalar separability criteria from positive but not completely positive maps. The concept is based on a decomposition of every positive map $\Lambda$ into a difference of two completely positive maps $\Lambda_1$, $\Lambda_2$, i.e., $\Lambda=\Lambda_1-\Lambda_2$. The scheme may be also treated as a generalization of the known entropic inequalities, which are obtained from the reduction map. An analysis performed on few classes of states shows that the new scalar criteria are stronger than the entropic inequalities and furthermore, when derived from indecomposable maps allow for detection of bound entanglement.