  Quantum entanglement plays a vital role in many quantum information and
communication tasks. Entangled states of higher dimensional systems are of
great interest due to the extended possibilities they provide. For example,
they allow the realisation of new types of quantum information schemes that can
offer higher information-density coding and greater resilience to errors than
can be achieved with entangled two-dimensional systems. Closing the detection
loophole in Bell test experiments is also more experimentally feasible when
higher dimensional entangled systems are used. We have measured previously
untested correlations between two photons to experimentally demonstrate
high-dimensional entangled states. We obtain violations of Bell-type
inequalities generalised to d-dimensional systems with up to d = 12.
Furthermore, the violations are strong enough to indicate genuine
11-dimensional entanglement. Our experiments use photons entangled in orbital
angular momentum (OAM), generated through spontaneous parametric
down-conversion (SPDC), and manipulated using computer controlled holograms.
