How to Observe High-Dimensional Two-Photon Entanglement with Only Two Detectors

Abstract

We propose a novel setup to investigate the entanglement of orbital angular momentum states living in a high-dimensional Hilbert space. We incorporate noninteger spiral phase plates in spatial analyzers, enabling us to use only two detectors. The two-photon states that are produced are not confined to a $2\times 2$-dimensional Hilbert space, and the setup allows the probing of correlations in a high-dimensional space. For the special case of half-integer spiral phase plates, we predict that the Clauser-Horne-Shimony-Holt-Bell parameter $S$ is larger than achievable for two qubits ($S=2\sqrt{2}$), namely, $S=3\frac{1}{5}$.