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.

空间纠缠是量子增强成像应用和高维量子信息协议的核心。特别是，对于成像和传感应用，需要具有宏观数量光子的量子态才能提供优于经典最新技术的真正优势。我们通过显示 EPR 空间（位置-动量）纠缠的存在，用明亮的双光束证明了爱因斯坦-波多尔斯基-罗森（EPR）悖论的原始位置和动量形式。电子倍增电荷耦合器件相机用于记录近场和远场区域中明亮双光束的图像，以实现对不确定性原理的明显违反超过一个数量级，即使在少量图像的限制。我们进一步表明，空间和时间自由度中量子相关性的存在导致近场和远场中明亮双光束的空间压缩。这提供了空间纠缠的另一个验证，并指出明亮的双光束中存在超纠缠。