Entanglement verification via nonlinear witnesses

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.