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.

中文翻译：

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基于噪声猜测解码的高效纠缠净化


在本文中，我们提出了一种基于散列和最近为经典纠错码设计的猜测随机加性噪声解码（GRAND）方法的新型二分纠缠净化协议。我们的协议比现有的哈希协议具有显着的优势，需要更少的量子位进行纯化，实现更高的保真度，并在降低计算成本的情况下提供更好的产量。我们提供数值和半分析结果来证实我们的发现，并与 Bennet 等人的哈希协议进行详细比较。尽管这项开创性的工作设计了性能界限，但它没有提供明确的实施结构。目前的工作填补了这一空白，提供了一种明确且更有效的纯化方法。我们证明，即使对于 16 对的小型集合，我们的协议也能够净化每个贝尔对 10% 左右的噪声状态。这项工作探索了基于测量的协议实现，以解决带有噪声的实际设置。这项工作为使用基于散列的方法和可行的计算成本实现实用且高效的纠缠纯化开辟了道路。与原始哈希协议相比，所提出的方法可以用最多小一百倍的初始资源来实现一些所需的保真度。因此，所提出的方法似乎非常适合资源数量有限的未来量子网络，并且计算开销相对较低。