2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/134585We consider a possible detector-efficiency loophole in experiments that detect entanglement via the local measurement of witness operators. Here, only local properties of the detectors are known. We derive a general threshold for the detector efficiencies which guarantees that a negative expectation value of a witness is due to entanglement, rather than to erroneous detectors. This threshold depends on the local decomposition of the witness and its measured expectation value. For two-qubit witnesses we find the local operator decomposition that is optimal with respect to closing the loophole.5 pages, 2 figures, published versionQuantum Physicstext