Deterministic Entanglement of Large-Scale Hermite-Gaussian Modes

Continuous-variable (CV) entanglement constitutes a powerful approach to deterministic quantum information protocols. Improving the scale of entanglement is of vital importance for enhancing the information capacity of quantum information protocols. Here we demonstrate the deterministic generation of CV entanglement of large-scale Hermite-Gaussian (HG) modes from the four-wave mixing (FWM) process in an atomic vapor. In our experiment, 56 pairs of entangled HG modes are deterministically and simultaneously generated from the FWM process, which increases the number of entangled spatial mode pairs in the CV system. Meanwhile, we experimentally verify the existence of CV entanglement between the evolution process from HG mode to Laguerre-Gaussian mode. Our results shed light on constructing high-capacity CV quantum information protocols and provide a promising platform to study CV entanglement.