  Detectors in the laboratory are often unlike their ideal theoretical cousins.
They have non-ideal efficiencies, which may then lead to non-trivial
implications. We show how it is possible to predict correct answers about
whether a shared quantum state is entangled in spite of finite detector
efficiencies, when the tool for entanglement detection is a nonlinear
entanglement witness. We first consider the detection loophole for shared
quantum states with nonpositive partial transpose. We subsequently find
nonlinear witness operators for bound entangled states with positive partial
transpose, and show how the detection loophole can be closed also in such
instances.
