Einstein-Podolsky-Rosen paradox with position-momentum entangled macroscopic twin beams

Spatial entanglement is at the heart of quantum enhanced imaging applications and high-dimensional quantum information protocols. In particular, for imaging and sensing applications, quantum states with a macroscopic number of photons are needed to provide a real advantage over the classical state-of-the-art. We demonstrate the Einstein-Podolsky-Rosen (EPR) paradox in its original position and momentum form with bright twin beams of light by showing the presence of EPR spatial (position-momentum) entanglement. An electron-multiplying charge-coupled-device camera is used to record images of the bright twin beams in the near and far field regimes to achieve an apparent violation of the uncertainty principle by more than an order of magnitude, which remains statistically significant even in the limit of a small number of images. We further show that the presence of quantum correlations in the spatial and temporal degrees of freedom leads to spatial squeezing of the bright twin beams in both the near and far fields. This provides another verification of the spatial entanglement and points to the presence of hyperentanglement in the bright twin beams.