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：量子理论允许多种信息处理与计算任务，而这些任务在经典系统中无法实现，因此对超越现有网络系统的量子互联网存在需求与应用。然而，功能性量子互联网的实现受限于基础性及实际挑战，例如量子系统传输中的高损耗、环境相互作用导致的退相干、量子态的脆弱性等。我们通过分析量子互联网扩展性与鲁棒性的限制，研究了这些约束条件的影响。针对量子网络，我们提出了安全通信、委托计算及端节点间资源分配的实际瓶颈。受图论（结合量子信息理论）抽象能力的启发，我们采用图论量化指标评估网络鲁棒性，并给出通信线路的关键阈值以实现量子互联网的有效通信。特别地，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实用性限制——尽管这类中继器可能对设备无关量子密钥分发有用。我们考虑了几种具有实际意义的量子网络，从连接遥远空间位置的卫星网络到当前可用的计算机量子处理器架构，并分析了其执行量子信息处理任务的鲁棒性。部分任务构成委托量子计算的原语，例如纠缠分发和量子隐形传态。针对某些量子网络示例，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、寻找端节点间最短路径，以及优化节点资源流。