Optimal entanglement witnesses for two qutrits

We provide a proof that entanglement witnesses considered recently in [D. Chru\'sci\'nski, F.A. Wudarski, arXiv:1105.4821] are optimal.Comment: 4 page

Exposed positive maps: a sufficient condition

Exposed positive maps in matrix algebras define a dense subset of extremal maps. We provide a sufficient condition for a positive map to be exposed. This is an analog of a spanning property which guaranties that a positive map is optimal. We analyze a class of decomposable maps for which this condition is also necessary