利用射影Cap构造极大纠缠的纠缠辅助量子纠错码

依据经典四元线性码理论和纠缠辅助量子纠错码理论,由四元线性码的生成矩阵给出四元线性码稳定极大纠缠的纠缠辅助量子码的几何特征。在给定几何特征基础上,由射影空间的Cap理论,设法用组合数学方法和搜索算法构造出给定几何特征的Cap,确定Cap码的参数。利用所得到的参数优良的Cap码,结合纠缠理论,构造出一些参数优良的极大纠缠的纠缠辅助量子码。其中,所构造的极大纠缠的纠缠辅助量子码有许多是最优码,还有一些纠缠辅助量子码改进了前人所得到的纠缠辅助量子码的参数,这些纠缠辅助量子纠错码是无法用已有方法得到的。这也证明了结合组合与搜索的方法来构造极大纠缠的纠缠辅助量子纠错码是有效的。

Construction of Entanglement-assisted Quantum Codes with Maximal Entanglement from Projective Caps

According to the entanglement-assisted quantum error-correcting code (EAQECC) theory, a geometry character of a quaternary linear code stabilized a maximal entanglement EAQECC is presented. On the basis of this character and the theory of Cap in projective space, methods for constructing such Caps by combinational mathematics and search algorithm are designed, and good codes from such Caps are determined. Many maximal entanglement EAQECCs are constructed from these obtained Cap codes. Almost all the maximal entanglement EAQECCs constructed here are optimal or near optimal EAQECCs, and some of them are the improved parameters of EAQECCs previously known; and some of them are new ones, but are very difficult to be obtained by using the known methods.