  The measurement of the position-momentum 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 letter, 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
measurement of position-momentum EPR correlations so far.
