  The controlled generation of entangled states and their subsequent detection
are integral aspects of quantum information science. In this work, we analyse
the application of nonlinear witnesses to the verification of entanglement, and
we demonstrate experimentally that nonlinear witnesses perform significantly
better than linear witnesses. Specifically, we demonstrate that a single non-
linear entanglement witness is able to determine to a high degree of certainty
that a mixed state containing orbital angular momentum (OAM) entanglement of
specific forms is entangled for any relative phase and sufficient fidelity.
This is a significant improvement over linear witnesses, which cannot provide
the same level of performance. We envisage that nonlinear witnesses and our
method of state preparation will have further uses in areas of quantum science
such as superdense coding and quantum key distribution.
