Data underlying the publication: Protocols for creating and distilling multipartite GHZ states with Bell pairs

The distribution of high quality Greenberger-Horne-Zeilinger (GHZ) states is at the heart of many quantum communication tasks, ranging from extending the baseline of telescopes to secret sharing. They also play an important role in error-correction architectures for distributed quantum computation, where Bell pairs can be leveraged to create an entangled network of quantum computers. We investigate the creation and distillation of GHZ states out of non-perfect Bell pairs over quantum networks. In particular, we introduce an algorithm based on dynamic programming to optimize over a large class of protocols that create and purify GHZ states. All protocols considered use a common framework based on measurements of non-local stabilizer operators of the target state (i.e., the GHZ state), where each non-local measurement consumes another (non-perfect) entangled state as a resource. The new protocols outperform previous proposals for scenarios without decoherence and local gate noise, by reducing the resources required to make high quality GHZ states. Furthermore, the algorithms can be applied for finding protocols for any number of parties and any number of entangled pairs involved.

高质量格林伯格-霍恩-蔡林格（Greenberger-Horne-Zeilinger，GHZ）态的分发是诸多量子通信任务的核心所在，其应用场景涵盖拓展望远镜基线、秘密共享等。此类态在分布式量子计算的纠错架构中同样发挥关键作用，在此类架构中可借助贝尔对（Bell pairs）构建量子计算机的纠缠网络。本研究针对量子网络中基于非理想贝尔对的GHZ态制备与蒸馏展开探究。具体而言，我们提出了一种基于动态规划（dynamic programming）的算法，可对一类用于制备并提纯GHZ态的协议进行优化。所有纳入考量的协议均采用一套通用框架：基于目标态（即GHZ态）的非局域稳定子算子（stabilizer operators）测量，其中每一次非局域测量都会消耗一个额外的（非理想）纠缠态作为资源。在无退相干（decoherence）与局部门噪声（local gate noise）的场景下，新型协议通过降低制备高质量GHZ态所需的资源消耗，性能优于此前的相关方案。此外，该算法可用于为任意参与方数量、任意纠缠对数量的场景设计协议。