Bi-PPT channels are entanglement breaking

Abstract: In a paper, Hirche and Leditzky introduced the notion of bi-PPT channels which are quantum channels that stay completely positive under composition with a transposition and such that the same property holds for one of their complementary channels. They asked whether there are examples of such channels that are not antidegradable. We show that this is not the case, since bi-PPT channels are always entanglement breaking. We also show that degradable quantum channels staying completely positive under composition with a transposition are entanglement breaking.