Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities

Bell’s theorem experiments, which test the completeness of quantum mechanics, have a number of loopholes. However, one type—detection loopholes—becomes smaller when the measurement has more possible outcomes. Bell’s inequality is now violated in tests with as many as 11 different results. Quantum entanglement 1 , 2 plays a vital role in many quantum-information and communication tasks 3 . Entangled states of higher-dimensional systems are of great interest owing to the extended possibilities they provide. For example, they enable the realization of new types of quantum information scheme that can offer higher-information-density coding and greater resilience to errors than can be achieved with entangled two-dimensional systems (see ref. 4 and references therein). Closing the detection loophole in Bell test experiments is also more experimentally feasible when higher-dimensional entangled systems are used 5 . We have measured previously untested correlations between two photons to experimentally demonstrate high-dimensional entangled states. We obtain violations of Bell-type inequalities generalized to d -dimensional systems 6 up to d =12. Furthermore, the violations are strong enough to indicate genuine 11-dimensional entanglement. Our experiments use photons entangled in orbital angular momentum 7 , generated through spontaneous parametric down-conversion 8 , 9 , and manipulated using computer-controlled holograms.