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We introduce the concept of Shannon dimensionality D as a new way to quantifybipartite entanglement as measured in an experiment. This is applied toorbital-angular-momentum entanglement of two photons, using two state analyzerscomposed of a rotatable angular-sector phase plate that is lens-coupled to asingle-mode fiber. We can deduce the value of D directly from the observedtwo-photon coincidence fringe. In our experiment, D varies between 2 and 6,depending on the experimental conditions. We predict how the Shannondimensionality evolves when the number of angular sectors imprinted in thephase plate is increased and anticipate that D = 50 is experimentally withinreach.

Shannon dimensionality of quantum channels and its application to photon entanglement