Degradable Strongly Entanglement Breaking Maps

In this paper, we provide a structure theorem and various characterizations of degradable strongly entanglement breaking maps on separable Hilbert spaces. In the finite dimensional case, we prove that unital degradable entanglement breaking maps are precisely the $C^{\ast }$-extreme points of the convex set of unital entanglement breaking maps on matrix algebras. Consequently, we get a structure for unital degradable positive partial transpose (PPT-) maps.