论文标题
网格网络中的纠缠路由和瓶颈
Entanglement Routing and Bottlenecks in Grid Networks
论文作者
论文摘要
在量子网络中，在多个用户中分发纠缠对对是一个基本问题。现有协议（例如（NPJ量子信息5，76（2019））中引入的$ x $协议）使用图理论工具（例如本地互补）来优化网络用户中提取任何铃铛对所需的测量数量。但是，这样的协议依靠找到用户之间的最短路径。在这里，现有结果是扩展的，以建立一个违反直觉的观念，即通常，执行$ x $协议的最佳途径不符合最短路径。该优势的具体示例是在小至12 QUAT的大小网络上提供的。还探索了在最近的邻居建筑中建立同时建立铃铛对的瓶颈。最近的结果表明，由于存在瓶颈的存在，线和环网对实施量子网络的不合适性被重新审视，并且使用图理论中的局部当量关系，这暗示了即使网格图也无法免除瓶颈问题。此外，注意到，此处获得的结果将用于分析基于测量的量子网络编码的优势。
Distributing entangled pairs among multiple users is a fundamental problem in quantum networks. Existing protocols like $X$ protocol introduced in (npj Quantum Information 5, 76 (2019)) use graph theoretic tools like local complementation to optimize the number of measurements required to extract any Bell pair among the network users. However, such a protocol relies on finding the shortest path between the users. Here, the existing results are extended to establish a counter-intuitive notion that, in general, the most optimal path to perform the $X$ protocol is not along the shortest path. Specific examples of this advantage are provided on networks of size as small as 12 qubits. Bottlenecks in establishing simultaneous Bell pairs in nearest-neighbor architectures are also explored. Recent results suggesting the unsuitability of the line and ring networks for the implementation of quantum networks due to the existence of bottlenecks are revisited, and using local equivalency relations from graph theory, it is hinted at the possibility that even grid graphs are not exempt from bottleneck issues. Further, it's noted that the results obtained here would be of use in analyzing the advantages of measurement-based quantum network coding.
