Assisted Entanglement Distillation

TL;DR

This paper introduces a novel assisted entanglement distillation protocol that leverages repeater stations to improve entanglement rates between two parties, outperforming traditional hierarchical strategies especially in complex tripartite states.

Contribution

It extends entanglement of assistance to mixed tripartite states and proposes a random coding protocol that surpasses the hashing bound in certain cases.

Findings

The protocol achieves higher entanglement rates than hashing bound for pure tripartite states.

Random measurement strategy outperforms hierarchical distillation in non-factorizable states.

Achievable rates are extended to scenarios with multiple repeaters helping two recipients.

Abstract

Motivated by the problem of designing quantum repeaters, we study entanglement distillation between two parties, Alice and Bob, starting from a mixed state and with the help of "repeater" stations. To treat the case of a single repeater, we extend the notion of entanglement of assistance to arbitrary mixed tripartite states and exhibit a protocol, based on a random coding strategy, for extracting pure entanglement. The rates achievable by this protocol formally resemble those achievable if the repeater station could merge its state to one of Alice and Bob even when such merging is impossible. This rate is provably better than the hashing bound for sufficiently pure tripartite states. We also compare our assisted distillation protocol to a hierarchical strategy consisting of entanglement distillation followed by entanglement swapping. We demonstrate by the use of a simple example that our random measurement strategy outperforms hierarchical distillation strategies when the individual helper stations' states fail to individually factorize into portions associated specifically with Alice and Bob. Finally, we use these results to find achievable rates for the more general scenario, where many spatially separated repeaters help two recipients distill entanglement.