General scheme for construction of scalar separability criteria from positive maps
Remigiusz Augusiak, Julia Stasińska · Physical Review A · 2008
We present a general scheme allowing for construction of scalar separability criteria from positive, but not completely positive, maps. The concept is based on a decomposition of every positive map $\ensuremath{\Lambda}$ acting on ${M}_{d}(\mathbb{C})$ into a difference of two completely positive maps ${\ensuremath{\Lambda}}_{1}$, ${\ensuremath{\Lambda}}_{2}$, i.e., $\ensuremath{\Lambda}={\ensuremath{\Lambda}}_{1}\ensuremath{-}{\ensuremath{\Lambda}}_{2}$. The scheme may also be treated as a generalization of the known entropic inequalities, which are obtained from the reduction map. Analyses performed on a few classes of states show that the scalar criteria are stronger than the entropic inequalities and when derived from indecomposable maps allow for detection of bound entanglement.