  Detecting quantumness of correlations (especially entanglement) is a very
hard task even in the simplest case i.e. two-partite quantum systems. Here we
provide an analysis whether there exists a relation between two most popular
types of entanglement identifiers: the first one based on positive maps and not
directly applicable in laboratory and the second one --- geometric entanglement
identifier which is based on specific Hermiticity-preserving maps. We show a
profound relation between those two types of entanglement criteria. Hereunder
we have proposed a general framework of nonlinear functional entanglement
identifiers which allows us to construct new experimentally friendly
entanglement criteria.
