Entanglement assisted quantum $(r,δ)$-locally recoverable codes

2026-08-17

AI Summary

本文解决了量子纠错码在纠删错误上的局限，通过引入纠缠辅助的量子(r,δ)局部可恢复码，并从多种经典码构造了最优纯纠缠辅助量子码。

Abstract

Quantum $(r,δ)$-locally recoverable codes are quantum error-correcting codes capable of correcting $δ-1$ qudit erasures within one subset of qudits of cardinality at most $r+δ-1$. In this paper, we introduce the more general framework of entanglement-assisted quantum $(r,δ)$-locally recoverable codes, assuming that the local recovery operation is assisted by receiver-held qudits that remain unaffected by erasures. We establish necessary and sufficient conditions for these codes to satisfy this property. For codes derived from Hermitian or Euclidean constructions, we establish connections between entanglement-assisted quantum and classical notions of $(r,δ)$-local recoverability, and derive a Singleton-like bound. Furthermore, we construct optimal pure entan\-gle\-ment-assisted quantum $(r,δ)$-locally recoverable codes from several families of classical codes, including bivariate $J$-affine variety codes, BCH codes, and homothetic-BCH codes.

Problem

• entanglement-assisted
• quantum error-correcting codes
• local recoverability
• qudit erasures

Innovation

• Entanglement-assisted
• Quantum codes
• Local recoverability
• Singleton-like bound
• Classical codes