In this paper, we propose a novel bipartite entanglement purification protocol built upon hashing and upon the guessing random additive noise decoding (GRAND) approach recently devised for classical error correction codes. Our protocol offers substantial advantages over existing hashing protocols, requiring fewer qubits for purification, achieving higher fidelities, and delivering better yields with reduced computational costs. We provide numerical and semi-analytical results to corroborate our findings and provide a detailed comparison with the hashing protocol of Bennet et al. Although that pioneering work devised performance bounds, it did not offer an explicit construction for implementation. The present work fills that gap, offering both an explicit and more efficient purification method. We demonstrate that our protocol is capable of purifying states with noise on the order of 10% per Bell pair even with a small ensemble of 16 pairs. The work explores a measurement-based implementation of the protocol to address practical setups with noise. This work opens the path to practical and efficient entanglement purification using hashing-based methods with feasible computational costs. Compared to the original hashing protocol, the proposed method can achieve some desired fidelity with a number of initial resources up to one hundred times smaller. Therefore, the proposed method seems well-fit for future quantum networks with a limited number of resources and entails a relatively low computational overhead.

翻译：本文提出了一种新颖的二分纠缠纯化协议，该协议建立在哈希编码以及最近为经典纠错码设计的猜测随机加性噪声解码（GRAND）方法之上。我们的协议相较于现有哈希协议具有显著优势：纯化所需量子比特更少，可实现更高保真度，且能以更低的计算成本获得更优产量。我们通过数值与半解析结果验证了上述发现，并与Bennet等人提出的哈希协议进行了详细比较。尽管该开创性工作推导了性能界，但未提供具体的实施方案。本研究填补了这一空白，给出了明确的且更高效的纯化方法。实验表明，即使仅使用16对贝尔态的小型集合，我们的协议也能纯化噪声水平高达每贝尔对10%的量子态。针对含噪声的实际场景，本文还探索了该协议的基于测量的实现方案。这项工作为利用哈希类方法实现实用化、高效化且计算成本可行的纠缠纯化开辟了道路。相较于原始哈希协议，本方法能以低至百分之一的初始资源数达到目标保真度。因此，该方法非常适用于资源受限的未来量子网络，且仅需较低的计算开销。