Breeding protocols are advantageous for finite-length entanglement distillation

TL;DR

This paper introduces a framework for converting stabilizer quantum error-correcting codes into breeding protocols, demonstrating that such protocols can outperform hashing in finite entanglement distillation scenarios.

Contribution

It generalizes previous conversion methods and provides an example where breeding protocols surpass hashing protocols for finite entanglement distillation.

Findings

Breeding protocols can be optimized using stabilizer codes.

A specific stabilizer code yields better finite entanglement distillation than hashing.

Finite entanglement distillation benefits from protocol conversion techniques.

Abstract

Bennett et al. proposed a family of protocols for entanglement distillation, namely, hashing, recurrence and breeding protocols. The last one is inferior to the hashing protocol in the asymptotic regime and has been investigated little. In this paper, we propose a framework of converting a stabilizer quantum error-correcting code to a breeding protocol, which is a generalization of the previous conversion methods by Luo-Devetak and Wilde. Then, show an example of a stabilizer that gives a breeding protocol better than hashing protocols, in which the finite number of maximally entangled pairs are distilled from the finite number of partially entangled pairs.