Deterministic high-rate entanglement distillation with neutral atom arrays

The goal of an entanglement distillation protocol is to convert large quantities of noisy entangled states into a smaller number of high-fidelity Bell pairs. The celebrated one-way hashing method is one such protocol, and it is known for being able to efficiently and deterministically distill entanglement in the asymptotic limit, i.e., when the size of the quantum system is very large. In this work, we consider setups with finite resources, e.g., a small fixed number of atoms in an atom array, and derive lower bounds on the distillation rate for the one-way hashing method. We provide analytical as well as numerical bounds on its entanglement distillation rate -- both significantly tighter than previously known bounds. We then show how the one-way hashing method can be efficiently implemented with neutral atom arrays. The combination of our theoretical results and the experimental blueprint we provide indicate that a full coherent implementation of the one-way hashing method is within reach with state-of-the-art quantum technology.