Most fundamental experiments in quantum mechanics have been performed with qubits, i.e. in rather low-dimensional Hilbert spaces. Various experimental techniques have recently opened up discrete higher dimensions for experiments. These are particularly multi-mode interference and photon states with more complex wavefronts, like orbital angular momentum (OAM) states.
In the talk, I will present some recent results focusing on OAM states and on verifications of entanglement in very high dimensions. So far, entanglement of quantum states with quantum numbers around 1,000 and of superposition in more than 100-dimensional Hilbert space have been realized. This may shed interesting light on the question of the quantum-classical transition. I will also discuss recent experiments for using some of these states in quantum communication with higher alphabets.
