This work investigates the use of quantum resources in distributed storage systems. Consider an $(n,k,d)$ distributed storage system in which a file is stored across $n$ nodes such that any $k$ nodes suffice to reconstruct the file. When a node fails, any $d$ helper nodes transmit information to a newcomer to rebuild the system. In contrast to the classical repair, where helper nodes transmit classical bits, we allow them to send classical information over quantum channels to the newcomer. The newcomer then generates its storage by performing appropriate measurements on the received quantum states. In this setting, we fully characterize the fundamental tradeoff between storage and repair bandwidth (total communication cost). Compared to classical systems, the optimal storage--bandwidth tradeoff can be significantly improved with the enhancement of quantum entanglement shared only among the surviving nodes, particularly at the minimum-storage regenerating point. Remarkably, we show that when $d \geq 2k-2$, there exists an operating point at which \textit{both storage and repair bandwidth are simultaneously minimized}. This phenomenon breaks the tradeoff in the classical setting and reveals a fundamentally new regime enabled by quantum communication.

翻译：本研究探讨了量子资源在分布式存储系统中的应用。考虑一个$(n,k,d)$分布式存储系统，其中文件被存储在$n$个节点上，使得任意$k$个节点足以重构文件。当节点失效时，任意$d$个辅助节点向新节点传输信息以重建系统。与经典修复中辅助节点传输经典比特不同，我们允许它们通过量子信道向新节点发送经典信息。新节点随后通过对接收到的量子态执行适当测量来生成其存储内容。在此设定下，我们完整刻画了存储与修复带宽（总通信成本）之间的基本权衡关系。与经典系统相比，仅通过幸存节点间共享的量子纠缠增强，最优存储-带宽权衡可得到显著改善，尤其在最小存储再生点处。值得注意的是，我们证明当$d \geq 2k-2$时，存在一个运行点使得\textit{存储与修复带宽同时达到最小化}。这一现象打破了经典设定中的权衡关系，揭示了由量子通信实现的全新机制。