Pixel Entanglement: Experimental Realization of Optically Entangled d=3 and d=6 Qudits

We demonstrate a simple experimental method for creating entangled qudits. Using transverse-momentum and position entanglement of photons emitted in spontaneous parametric down-conversion, we show entanglement between discrete regions of space, i.e., pixels. We map each photon onto as many as six pixels, where each pixel represents one level of our qudit state. The method is easily generalizable to create even higher dimensional, entangled states. Thus, the realization of quantum information processing in arbitrarily high dimensions is possible, allowing for greatly increased information capacity.