As quantum theory allows for information processing and computing tasks that otherwise are not possible with classical systems, there is a need and use of quantum Internet beyond existing network systems. At the same time, the realization of a desirably functional quantum Internet is hindered by fundamental and practical challenges such as high loss during transmission of quantum systems, decoherence due to interaction with the environment, fragility of quantum states, etc. We study the implications of these constraints by analyzing the limitations on the scaling and robustness of quantum Internet. Considering quantum networks, we present practical bottlenecks for secure communication, delegated computing, and resource distribution among end nodes. Motivated by the power of abstraction in graph theory (in association with quantum information theory), we consider graph-theoretic quantifiers to assess network robustness and provide critical values of communication lines for viable communication over quantum Internet. In particular, we begin by discussing limitations on usefulness of isotropic states as device-independent quantum key repeaters which otherwise could be useful for device-independent quantum key distribution. We consider some quantum networks of practical interest, ranging from satellite-based networks connecting far-off spatial locations to currently available quantum processor architectures within computers, and analyze their robustness to perform quantum information processing tasks. Some of these tasks form primitives for delegated quantum computing, e.g., entanglement distribution and quantum teleportation. For some examples of quantum networks, we present algorithms to perform different quantum network tasks of interest such as constructing the network structure, finding the shortest path between a pair of end nodes, and optimizing the flow of resources at a node.

翻译：量子理论能够实现经典系统无法完成的信息处理与计算任务，这使得量子互联网在现有网络系统之外具有显著需求与应用价值。然而，理想功能型量子互联网的实现受到诸多基础性与实践性挑战的制约，例如量子系统传输过程中的高损耗、环境相互作用导致的退相干、以及量子态的脆弱性等。本文通过分析量子互联网在可扩展性与鲁棒性方面的限制，系统研究了这些约束条件的内在影响。针对量子网络，我们揭示了端节点间安全通信、委托计算及资源分配中的实际瓶颈。受图论（与量子信息论相结合）抽象能力的启发，我们采用图论量化指标评估网络鲁棒性，并给出可行量子互联网通信所需的关键通信线路阈值。具体而言，我们首先探讨了各向同性态作为设备无关量子密钥中继器的效用局限性——尽管此类态本可用于设备无关量子密钥分发。我们研究了从连接远距离空间位置的卫星网络到当前计算机中量子处理器架构等若干具有实际意义的量子网络，分析了它们执行量子信息处理任务时的鲁棒性。其中部分任务构成委托量子计算的基本原语，例如纠缠分发与量子隐形传态。针对若干量子网络实例，我们提出了执行不同量子网络任务的算法，包括构建网络拓扑、寻找端节点间最短路径以及优化节点资源流动。