Position Correlation Enabled Quantum Imaging with Undetected Photons

Quantum imaging with undetected photons (QIUP) is a unique imaging technique that does not require the detection of the light used for illuminating the object. The technique requires a correlated pair of photons. In the existing implementations of QIUP, the imaging is enabled by the momentum correlation between the twin photons. We investigate the complementary scenario in which the imaging is instead enabled by the position correlation between the two photons. We present a general theory and show that the properties of the images obtained in these two cases are significantly distinct.