  Single photons with helical phase structures may carry a quantized amount of
orbital angular momentum (OAM) and their entanglement is important for quantum
information science and fundamental tests of quantum theory. Because there is
no theoretical upper limit on how many quanta of OAM a single photon can carry,
it is possible to create entanglement between two particles with an arbitrary
high difference in the quantum number. By transferring polarization
entanglement to OAM with an interferometric scheme, we generate and verify
entanglement up to 600 quanta difference in the orbital angular momentum. The
only restrictive factors towards higher numbers are current technical
limitations. We also experimentally demonstrate that the entanglement of very
high OAM can improve the sensitivity of the angular resolution in remote
sensing.
