Breeding protocols are advantageous for finite-length entanglement distillation
Ryutaroh Matsumoto
TL;DR
This work addresses the finite-length advantage of breeding entanglement distillation protocols (EDPs) over hashing by extending stabilizer-code–to–EDP conversions through the inclusion of complex conjugation, enabling non-real encoding operators. It develops a constructive framework that maps entanglement-assisted quantum error-correcting codes (EAQECCs) to breeding EDPs, producing net entanglement of $k-c$ from $n$ noisy pairs plus $c$ shared ebits when $2t+e<d$. The authors demonstrate a concrete example using a pure $[[6,4,2]]_p$ stabilizer code that yields better finite-length distillation than any hashing protocol, illustrating the practical potential of their approach. They also outline future directions, including incorporating two-way classical communication (2-CC) to further improve performance and broaden applicability of breeding EDPs.
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.