Classical locally recoverable codes (LRCs) have become indispensable in distributed storage systems. They provide efficient recovery in terms of localized errors. Quantum LRCs have very recently been introduced for their potential application in quantum data storage. In this paper, we use classical LRCs to investigate quantum LRCs. We prove that the parameters of quantum LRCs are bounded by their classical counterparts. We deduce the bounds on the parameters of quantum LRCs from the bounds on the parameters of the classical ones. We establish a characterization of optimal pure quantum LRCs based on classical codes with specific properties. Using well-crafted classical LRCs as ingredients in the construction of quantum CSS codes, we offer the first construction of several families of optimal pure quantum LRCs.

翻译：经典局部可恢复码（LRCs）已成为分布式存储系统中不可或缺的组成部分，其能针对局部化错误提供高效恢复。量子局部可恢复码（量子LRCs）近期因在量子数据存储中的潜在应用而被提出。本文利用经典LRCs研究量子LRCs，证明量子LRCs的参数受其经典对应物的界限制，并由此推导出量子LRCs的参数界。我们基于具有特定性质的经典码，建立了最优纯量子LRCs的刻画方法。通过将精心设计的经典LRCs作为量子CSS码的构造单元，首次实现了多个系列最优纯量子LRCs的构造。