Structural approximations to positive maps and entanglement-breaking channels

Structural approximations to positive, but not completely positive maps are approximate physical realizations of these nonphysical maps. They find applications in the design of direct entanglement-detection methods. We show that many of these approximations, in the relevant case of optimal positive maps, define an entanglement breaking channel and, consequently, can be implemented via a measurement and state-preparation protocol. We also show how our findings can be useful for the design of better and simpler direct entanglement detection methods.