Efficient nonlinear witnessing of non–absolutely separable states with lossy detectors

Entangled states are undoubtedly an integral part of various quantum information processing tasks. On the other hand, absolutely separable which cannot be made entangled under any global unitary operations useless from resource theoretic perspective, and hence identifying non-absolutely can important issue for designing technologies. Here we report that nonlinear witness operators provide significant improvements in detecting over their linear analogs, by invoking examples dimensions. We also address problem closing detection loophole find critical efficiency detectors above no fake (non-absolutely positive partial transposed) is possible.