Measuring Entanglement using Programmable Holograms

The Einstein–Podolsky–Rosen (EPR) paradox proposes an entangled quantum state in high dimensional non-commuting observables, position and momentum. We experimentally demonstrate a novel method for measuring spatial correlations in joint position and joint momentum space for entangled photons in an EPR-like state. Research in the field of quantum optics can provide insight into quantum information processing, communication, quantum key distribution, and further investigation into the EPR paradox and locality. Unlike existing techniques, we take measurements of non-commuting observables using a static configuration. A 405nm pump laser incident on a Bismuth Borate nonlinear crystal produces an EPR state as a pair of 810nm photons through the process of spontaneous parametric downconversion. To measure spatial correlations, we take advantage of holograms displayed on digital micromirror devices (DMDs). This method allows for control over the basis that is measured only by changing what hologram is displayed on the DMD, without having to add lenses or other bulk optic components. The field interaction that generates a hologram can be computationally simulated and displayed on the DMD allowing for a momentum mode projection onto the incident state. Collection of joint position and joint momentum correlations provide an entanglement witness. Verification of entanglement using this technique provides the framework to investigate projections onto arbitrary states and explore further quantum communication advances