Constant Overhead Entanglement Distillation via Scrambling

TL;DR

This paper introduces a novel entanglement distillation protocol using quantum scrambling that achieves constant resource overhead, is practical with shallow circuits, and outperforms existing methods in high-fidelity quantum networking.

Contribution

The authors develop a scrambling-based entanglement distillation protocol with constant overhead and shallow circuit requirements, improving practicality and performance over prior schemes.

Findings

Achieves asymptotically constant overhead independent of target error rate.

Implementable with shallow quantum circuits of polylogarithmic depth.

Requires only 7 noisy inputs to reach extremely high fidelity from 10% initial infidelity.

Abstract

High-fidelity quantum entanglement enables key quantum networking capabilities such as secure communication and distributed quantum computing, but long-distance entanglement distribution is limited by noise and loss. Entanglement distillation protocols address this problem by extracting high-fidelity Bell pairs from multiple noisy ones. The primary objective is minimizing the resource overhead: the number of noisy input pairs needed to distill each high-fidelity output pair. While protocols achieving optimal overhead are known in theory, they often require complex decoding operations that make practical implementation challenging. We circumvent this challenge by introducing protocols that use quantum scrambling -- the spreading of quantum information under chaotic dynamics -- through random Clifford operations. Based on this scrambling mechanism, our protocol maintains asymptotically \emph{constant} overhead, independent of the desired output error rate $\bar{\varepsilon}$, and can be implemented with shallow quantum circuits of depth $O(\mathrm{poly} \log \log \bar{\varepsilon}^{-1})$ and memory $O(\mathrm{poly} \log \bar{\varepsilon}^{-1})$. Our protocol remains effective even with noisy quantum gates. By incorporating error correction, our protocol achieves state-of-the-art performance: starting with pairs of 10% initial infidelity, we require only 7 noisy inputs per output pair to distill a single Bell pair with infidelity $\bar{\varepsilon}=10^{-12}$, substantially outperforming existing schemes. We demonstrate the utility of our protocols for quantum repeater networks.