Entanglement-assisted quantum locally recoverable codes: bounds and constructions with availability

• URL: http://arxiv.org/abs/2608.09886v2
• Date: Tue, 11 Aug 2026 07:07:58 GMT
• Title: Entanglement-assisted quantum locally recoverable codes: bounds and constructions with availability
• Abstract summary: We define entanglement-assisted quantum locally recoverable codes with availability.<n>Any set of up to $-1$ erased qudits can be recovered from any one of $t$ local recovery sets.
• Score: 3.3135760457470713
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this work, we define entanglement-assisted quantum locally recoverable codes with availability, in which any set of up to $δ-1$ erased qudits can be recovered from any one of $t$ local recovery sets, each of size at most $r+δ-1$, with the recovery sets intersecting exactly in the erased coordinates, where $r$ is a (small) positive integer. We show that shared entanglement permits $t>1$, meaning that multiple local recovery sets can be available for the same set of up to $δ-1$ erasures. We establish a Singleton-like bound for this family of codes and present random constructions based on classical linear codes with Vandermonde parity-check matrices. We also provide explicit constructions of entanglement-assisted quantum locally recoverable codes with availability from several classical code families and their folded versions, including Tamo-Barg codes, fiber-product codes, and algebraic-geometry codes such as one-point Hermitian and Suzuki codes.

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