  Optomechanical systems open new possibilities in fundamental research at the
interface between quantum information and gravity. Recently, an ambitious
experimental proposal was suggested by Bose et al. to measure the entanglement
between two optomechanical systems generated by their gravitational
interaction. The scheme relies on witnessing entanglement between the two
systems. Here we develop a general framework to study the quality of bipartite
entanglement witnesses using fidelity witnesses. We then apply this framework
to the gravitational entanglement proposal, optimizing for the detection of
entanglement. We construct a witness consisting of only 5 non-trivial spin
measurements, which we compare with other proposed witnesses. With
post-processing our witness can detect entanglement for any choice of phases in
the setup, up to a set of measure zero.
