  Entanglement witnesses are invaluable for efficient quantum entanglement
certification without the need for expensive quantum state tomography. Yet,
standard entanglement witnessing requires multiple measurements and its bounds
can be elusive as a result of experimental imperfections. Here we introduce and
demonstrate a novel procedure for entanglement detection which seamlessly and
easily improves any standard witnessing procedure by using additional available
information to tighten the witnessing bounds. Moreover, by relaxing the
requirements on the witness operators, our method removes the general need for
the difficult task of witness decomposition into local observables. We
experimentally demonstrate entanglement detection with our approach using a
separable test operator and a simple fixed measurement-device for each agent.
Finally we show that the method can be generalized to higher-dimensional and
multipartite cases with a complexity that scales linearly with the number of
parties.
