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：由于量子理论允许实现经典系统无法完成的信息处理与计算任务，因此对量子互联网的需求及其应用已超越现有网络体系。然而，理想功能化量子互联网的实现受到诸多基础性与现实性挑战的阻碍，例如量子系统传输过程中的高损耗、与环境相互作用导致的退相干、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稳健性方面的局限，探讨这些约束条件的内在影响。针对量子网络，我们揭示了安全通信、委托计算及终端节点间资源分配所面临的实际瓶颈。受图论抽象能力（结合量子信息理论）的启发，我们采用图论量化指标评估网络稳健性，并为量子互联网可行通信提供通信线路的临界值。具体而言，我们首先讨论各向同性态作为设备无关量子密钥中继器的效用局限——尽管该态在设备无关量子密钥分发中具有潜在价值。我们考察了若干具有实际意义的量子网络案例，涵盖连接遥远空间位置的卫星网络至当前计算机内可用的量子处理器架构，并分析其执行量子信息处理任务的稳健性。其中部分任务构成委托量子计算的基础原语，例如纠缠分发与量子隐形传态。针对某些量子网络实例，我们提出了执行不同量子网络任务的算法，包括构建网络结构、寻找终端节点对之间的最短路径以及优化节点资源流。