General scheme for construction of scalar separability criteria from positive maps
Remigiusz Augusiak and Julia Stasi\'{n}ska

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 $\Lambda$ acting on $M_{d}(\mathbb{C})$ 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. Analyses performed on few classes of states shows that the new scalar criteria are stronger than the entropic inequalities and when derived from indecomposable maps allow for detection of bound entanglement.

© 2008 The American Physical Society.