Entanglement-assisted quantum locally recoverable codes: bounds and constructions with availability
2026-08-10 • Information Theory
Information Theory
AI summaryⓘ
The authors introduce a new type of quantum error-correcting code called entanglement-assisted quantum locally recoverable codes with availability. These codes allow recovering lost quantum data (up to δ-1 erased qudits) from multiple different small groups of qudits, thanks to shared entanglement between sender and receiver. They prove a fundamental limit similar to the classical Singleton bound for these codes and give both random and explicit methods to build them using known classical code families like Tamo-Barg and algebraic-geometry codes. Their work shows that shared entanglement can help improve the flexibility of quantum data recovery.
quantum error correctionentanglement-assisted codeslocally recoverable codesavailabilityquantum erasuresSingleton boundclassical linear codesTamo-Barg codesalgebraic-geometry codesVandermonde matrices
Authors
Gretchen L. Matthews, Julia Shapiro
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.