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.

翻译：Bennett等人提出了一系列纠缠蒸馏协议族，包括哈希协议、递归协议和有性繁殖协议。其中，有性繁殖协议在渐近极限下的性能逊于哈希协议，因此相关研究较少。本文提出了一种将稳定子量子纠错码转换为有性繁殖协议的框架，这是对Luo-Devetak和Wilde先前转换方法的推广。随后，我们给出一个稳定子实例，该实例生成的有性繁殖协议优于哈希协议，能够在有限数量的部分纠缠对中蒸馏出有限数量的最大纠缠对。