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