Closing loopholes of measurement-device-independent nonlinear entanglement witnesses

The concept of entanglement witnesses forms a useful technique to detect entanglement in realistic quantum devices. Measurement-device-independent nonlinear entanglement witnesses (MDI-NEWs) are a kind of entanglement witness that eliminates dependence on the correct alignments of measurement devices for guaranteeing the existence of entanglement and also detects more entangled states than its linear counterparts. While this method guarantees entanglement independent of measurement alignments, it is still prone to serving wrong results due to other loopholes. Here, we study the response of MDI-NEWs to two categories of faults occurring in experiments. In the first category, the detection loophole, characterized by lost and additional events of outcomes of measurements, is investigated, and bounds which guarantee entanglement are obtained in terms of the efficiency of measurement being performed. In the second category, we study noise associated with the sets of additional quantum inputs required in MDI-NEW scenarios. In this case, a type of noise is identified which still allows the MDI-NEWs to guarantee entanglement. We also show that MDI-NEWs are less or equally robust in comparison to their linear counterparts under the same noise in additional quantum inputs, although the former group detects a larger volume of entangled states in the noiseless scenario than their linear cousins.