[论文解读] Multiparty quantum protocols for assisted entanglement distillation

Nicolas Dutil|arXiv (Cornell University)|May 23, 2011

Quantum Information and Cryptography参考文献 77被引用 12

一句话总结

本文提出了一种基于随机编码策略的多用户量子协议，用于辅助式纠缠浓缩，将辅助纠缠的概念扩展至任意三体态。该协议在无需时分复用的情况下，实现了渐近最优的浓缩速率，利用光滑极小和极大熵分析了一次性情形下的纠缠代价，从而实现了长距离量子通信中高效量子中继网络的构建。

ABSTRACT

Quantum information theory is a multidisciplinary field whose objective is to understand what happens when information is stored in the state of a quantum system. Quantum mechanics provides us with a new resource, called quantum entanglement, which can be exploited to achieve novel tasks such as teleportation and superdense coding. Current technologies allow the transmission of entangled photon pairs across distances up to roughly 100 kilometers. For longer distances, noise arising from various sources degrade the transmission of entanglement to the point that it becomes impossible to use the entanglement as a resource for future tasks. A strategy for dealing with this difficulty is to employ quantum repeaters, stations intermediate between the sender and receiver which participate in the process of entanglement distillation, thereby improving on what the sender and receiver could do on their own. In this work, we study entanglement distillation between two recipients sharing a mixed state and with the help of repeater stations. We extend the notion of entanglement of assistance to arbitrary states and give a protocol for extracting pure entanglement. We also study quantum communication protocols in a more general context. We give a new protocol for the task of multiparty state merging. The previous multiparty state merging protocol required the use of time-sharing. Our protocol does not require time-sharing for distributed compression of two senders. In the one-shot regime, we achieve multiparty state merging with entanglement costs not restricted to corner points of the entanglement cost region. Our analysis of the entanglement cost is performed using (smooth) min- and max-entropies. We illustrate the benefits of our approach by looking at different examples.

研究动机与目标

• 设计一种在存在多个中间中继站的场景下可扩展的多用户量子协议，用于纠缠浓缩。
• 将辅助纠缠的概念从双体系统扩展至任意三体量子态。
• 在一次性情形下实现高比率的纠缠浓缩，且无需依赖时分复用策略。
• 利用光滑极小和极大熵分析分布式量子通信中多用户态传输的纠缠代价。

提出的方法

• 提出一种基于典型子空间和哈尓测度上酉平均的随机测量协议，用于多用户态合并。
• 应用相对参考系的去耦合概念，实现在无需时分复用情况下的分布式压缩。
• 利用（光滑）极小和极大熵刻画一次性情形下的纠缠代价。
• 采用典型性论证和迹范数界，确保测量后态收敛至典型态。
• 提出一种分拆传输协议，适用于两个发送方和多个接收方，实现共享态传输且纠缠开销最小化。
• 结合马尔可夫不等式与并集界，推导出随机测量后态保真度的高概率界。

实验结果

研究问题

• RQ1 在存在多个中间中继站的多用户环境中，能否高效实现纠缠浓缩？
• RQ2 如何将辅助纠缠的概念从双体系统推广至任意三体态？
• RQ3 在一次性情形下，能否在不使用时分复用的情况下实现多用户态合并？
• RQ4 利用光滑熵进行分布式态传输时，可实现的纠缠代价是什么？
• RQ5 随机测量策略能否在最小资源开销下实现高保真度的纠缠浓缩？

主要发现

• 该协议实现了一次性多用户态合并，其纠缠代价不受代价区域角落点的限制，从而实现了更灵活的资源分配。
• 对于较大的 $ n $，该协议确保接收方的测量后态与典型态之间的迹距离为 $ \tilde{O}(1/\text{poly}(n)) $，且概率很高。
• 浓缩过程的平均保真度随着 $ n \to \infty $ 而收敛至 1，误差概率受 $ \alpha $ 限制，该值可被任意缩小。
• 在典型子空间上使用随机测量，使协议能够绕过分布式压缩任务中对时分复用的需求。
• 分析表明，纠缠代价由光滑极小和极大熵决定，提供了紧致的操作表征。
• 该协议在存在多个中继站的情况下，实现了辅助纠缠的渐近最优浓缩速率，将先前结果推广至一般多体情形。