Measurement of two-photon position-momentum Einstein-Podolsky-Rosen correlations through single-photon intensity measurements

The measurement of the position-momentum Einstein-Podolsky-Rosen (EPR) correlations of a two-photon state is important for many quantum information applications ranging from quantum key distribution to coincidence imaging. However, all the existing techniques for measuring the position-momentum EPR correlations involve coincidence detection and thus suffer from issues that result in less accurate measurements. In this article, we propose and demonstrate an experimental scheme that does not require coincidence detection for measuring the EPR correlations. Our technique works for two-photon states that are pure, irrespective of whether the state is separable or entangled. We theoretically show that if the pure two-photon state satisfies a certain set of conditions then the position-momentum EPR correlations can be obtained by doing the intensity measurements on only one of the photons. We experimentally demonstrate this technique for pure two-photon states produced by type-I spontaneous parametric down-conversion, and to the best of our knowledge, we report the most accurate experimental measurement of position-momentum EPR correlations.