Bounds and Constructions of Quantum Locally Recoverable Codes from Quantum CSS Codes

TL;DR

This paper explores bounds and constructions of quantum locally recoverable codes (LRCs) using classical LRCs and CSS codes, establishing parameter bounds and presenting new optimal quantum LRC families.

Contribution

It derives bounds on quantum LRC parameters from classical bounds and constructs new optimal pure quantum LRCs using classical codes within the CSS framework.

Findings

Quantum LRC parameters are bounded by classical LRC bounds.

Characterization of optimal pure quantum LRCs based on classical codes.

First constructions of several families of optimal pure quantum LRCs.

Abstract

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.