One-Way Hashing Method with Finite Resources*

The one-way hashing method refers to a well-known entanglement distillation protocol that can be used to transform multiple copies of a bipartite state into high fidelity Bell pairs, using only local operations and classical communication. While it is known that this protocol is very effective at distilling entanglement from large-scale systems, previous results indicated that the one-way hashing method may not be useful when the number of initial copies is small. For this reason, the protocol has not yet been realized by any experimental setup. By leveraging properties of the Hartley entropy, we provide significantly improved analytical lower bounds on this protocol's distillation rate, as well as numerical simulations, which demonstrate that entanglement can be distilled via the one-way hashing method at a higher rate and using fewer initial copies than previously expected. These results show that the one-way hashing method is not only of interest for future large-scale quantum networks; it is also a viable option for distilling entanglement on state-of-the-art quantum technologies.