Precise quantum tomography of photon pairs with entangled orbital angular momentum

We report a high fidelity tomographic reconstruction of the quantum state of photon pairs generated by parametric down-conversion with orbital angular momentum (OAM) entanglement. Our tomography method allows us to estimate an upper and lower bound for the entanglement between the down-converted photons. We investigate the two-dimensional state subspace defined by the OAM states ±l and superpositions thereof, with l=1, 2, ..., 30. We find that the reconstructed density matrix, even for OAMs up to around l=20, is close to that of a maximally entangled Bell state with a fidelity in the range between F=0.979 and F=0.814. This demonstrates that, although the single count-rate diminishes with increasing l, entanglement persists in a large dimensional state space.