Optimized Detection of High-Dimensional Entanglement

Entanglement detection is one of the most conventional tasks in quantum information processing. While most experimental demonstrations of high-dimensional entanglement rely on fidelity-based witnesses, these are powerless to detect entanglement within a large class of entangled quantum states, the so-called unfaithful states. In this Letter, we introduce a highly flexible automated method to construct optimal tests for entanglement detection given a bipartite target state of arbitrary dimension, faithful or unfaithful, and a set of local measurement operators. By restricting the number or complexity of the considered measurement settings, our method outputs the most convenient protocol which can be implemented using a wide range of experimental techniques such as photons, superconducting qudits, cold atoms, or trapped ions. With an experimental quantum optics setup that can prepare and measure arbitrary highdimensional mixed states, we implement some three-setting protocols generated by our method. These protocols allow us to experimentally certify two- and three-unfaithful entanglement in four-dimensional photonic states, some of which contain well above 50% of noise.