Optimal witnesses detecting positive-partial-transpose entangled states in Cn ⊗ Cn

Recently, Qi and Hou [Phys. Rev. A 85, 022334 (2012)] provided optimal entanglement witnesses without the spanning property. These witnesses are associated with indecomposable positive linear maps, but whether partial transposes of these witnesses are also optimal has not been evaluated. We show that partial transposes of these entanglement witnesses have the spanning property and that these witnesses are indeed optimal witnesses detecting positive-partial-transposed entangled states (nondecomposable optimal entanglement witnesses).