2024/12/21 by Galindo, Carlos, Hernando, Fernando, Martín-Cruz, Helena +1 · 5 citations
#11T71 #81P45 #94B65 #FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2412.16590
Classical (r,δ)-locally recoverable codes are designed for avoiding loss of information in large scale distributed and cloud storage systems. We introduce the quantum counterpart of those codes by defining quantum (r,δ)-locally recoverable codes which are quantum error-correcting codes capable of correcting δ-1 qudit erasures from sets of at most r+ δ-1 qudits. We give a necessary and sufficient condition for a quantum stabilizer code Q(C) to be (r,δ)-locally recoverable. Our condition depends only on the puncturing and shortening at suitable sets of both the symplectic self-orthogonal code C used for constructing Q(C) and its symplectic dual C⊥s. When Q(C) comes from a Hermitian or Euclidean dual-containing code, and under an extra condition, we show that there is an equivalence between the classical and quantum concepts of (r,δ)-local recoverability. A Singleton-like bound is stated in this case and examples attaining the bound are given.