Experimental measurement-device-independent high dimensional entanglement quantification

The certification and quantification of entanglement are of great importance in characterizing entangled systems. Measurement-device-independent entanglement witness (MDIEW) has been developed to solve the problem of imperfection of measurement schemes and has been used to witness entangled qubit systems in the lab. A recent paper showed MDIEW can be also used to quantify entanglement of a d-dimensional state according to standard entanglement measures, without prior information of the quantum state. Here, we report the first experimental demonstration of a high dimensional MDIEW game on a 3-level bipartite state and observation of a lower bound on the generalized robustness measure that excludes the bound of 2-dimensional systems. We further demonstrate this quantification process can act as a MDI dimension witness (MDIDW). Using the MDIDW, we certify the presence of our system of dimension (at least) $d=3$.