 Decomposable positive map

A decomposable positive map between complex matrix algebras has the form $\Phi ={\Phi }_1+{\Phi }_2\circ T$, where ${\Phi }_1,{\Phi }_2$ are completely positive maps and $T$ is the matrix transpose. Such a map cannot detect a positive partial transpose entangled state: applying it to one subsystem gives a sum of two positive operators.