In this paper, we provide a framework for constructing entanglement-assisted quantum error-correcting codes (EAQECCs) from classical additive codes over a finite commutative local Frobenius ring. We derive a formula for the minimum number of entanglement qudits required to construct an EAQECC from a linear code over the ring $\mathbb{Z}_{p^s}$. This is used to obtain an exact expression for the minimum number of entanglement qudits required to construct an EAQECC from an additive code over a Galois ring, which significantly extends known results for EAQECCs over finite fields.

翻译：在本文中, 我们提供了一个框架, 用于构建由传统添加编码组成的缠绕辅助量子误差校正代码( EAQECCs), 用于构建一个固定的折叠式本地Frobenius环。 我们从以$\ mathb ⁇ p ⁇ s} 环为单位的线性代码中, 得出构建 EAQECC 所需最小量的折叠式方程式。 用于获取一个精确表达法, 用于构建 EAQECC 所需的最小量的缠绕矩码, 以加洛瓦环为单位, 它将已知的EAQECCs结果大大扩展至限定面积。