Measurement-induced relative-position localization through entanglement

We consider the localization of a pair of particles in relative-position space. We show how a sequence of scattering interactions progressively entangles two particles, giving rise to a robust state of well-defined separation and thus providing a natural description of relative position. We use two thought experiments to describe the localization process. The first is an interferometer with recoiling mirrors. The second, and more general, case considers photons scattering from a pair of particles and the resulting emergence of a Young's interference pattern. The underlying framework of the localization process suggests a prominent role for entanglement and relative observables at the boundary between quantum and classical mechanics.