论文标题
本地Frobenius环上的纠缠辅助量子误差校正代码
Entanglement-Assisted Quantum Error-Correcting Codes over Local Frobenius Rings
论文作者
论文摘要
在本文中，我们提供了一个框架，用于通过有限的可交换性的本地frobenius ring $ \ MATHCAL {R} $构建经典添加剂代码的纠缠辅助量子错误校正代码（EAQECC）。框架的核心，这是我们论文的主要技术贡献之一，是构建添加代码$ \ MATHCAL {C} $上$ \ Mathcal {r} $的过程，这是一种用于$ \ Mathcal {C} $的生成集，这是标准形式，这是标准形式，这意味着它具有纯粹的纯度生成和超级脂肪生成的生成和超级脂肪的生成。此外，当$ \ Mathcal {r} $是一个Galois环时，我们为从$ \ Mathcal {r} $上构造EAQECC所需的最小最大纠缠的Qudits的最小对数，这是EAQECC的已知结果，而EAQECC的已知结果超过了有限的。我们还展示了如何在添加剂代码中添加额外的坐标，可以使我们在确定由我们的构造产生的EAQECC的参数时具有一定程度的灵活性。
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 $\mathcal{R}$. At the heart of the framework, and this is one of the main technical contributions of our paper, is a procedure to construct, for an additive code $\mathcal{C}$ over $\mathcal{R}$, a generating set for $\mathcal{C}$ that is in standard form, meaning that it consists purely of isotropic generators and hyperbolic pairs. Moreover, when $\mathcal{R}$ is a Galois ring, we give an exact expression for the minimum number of pairs of maximally entangled qudits required to construct an EAQECC from an additive code over $\mathcal{R}$, which significantly extends known results for EAQECCs over finite fields. We also demonstrate how adding extra coordinates to an additive code can give us a certain degree of flexibility in determining the parameters of the EAQECCs that result from our construction.
