Increasing the complexity of entangled states by expanding their dimensionality allows the implementation of novel fundamental tests of nature (such as “All-versus-Nothing”-tests of local realism), and enables genuinely new protocols for quantum information (for example, high-dimensional QKD).
Here I will talk about three experiments that exploit high-dimensional Hilbert-spaces in different ways. The first one uses the spatial degree of freedom of entangled photons. By applying a novel nonlinear entanglement witness, high-dimensional entanglement was verified in a source-independent way. The second experiment can create a variety of different path-entangled states, and is able to perform any local unitary transformation. Finally, the third experiment creates and verifies entanglement of photons with very high quanta of angular momentum.