标题： 混合字母表上的量子纠错码 显示英文标题

标题： Quantum Error-Correcting Codes over Mixed Alphabets

摘要： 在所有量子信息任务过程中不可避免地会出现错误，量子纠错码（QECC）是应对各种量子噪声的强大工具。 对于标准的QECC，物理系统具有相同数量的能量级。 在这里，我们将提出混合字母表上的QECC，即不同维度的物理系统，并研究它们的构造及其量子Singleton界。 我们提出了两种构造方法：基于图论对象复合编码团的图形构造和基于投影的构造。 我们通过使用两个字母表来说明我们的想法，即找出一些在混合字母表上的一次纠错或检测码，例如最优的$((6,8,3))_{4^52^1}$、$((6,4,3))_{4^42^2}$和$((5,16,2))_{4^32^2}$码以及次优的$((5,9,2))_{3^42^1}$码。 我们的方法也为标准QECC的构造提供了启示，例如最优$((6,16,3))_4$码的构造以及最优$((2n+3,p^{2n+1},2))_{p}$码与$p=4k$的构造。 显示英文摘要

摘要： Errors are inevitable during all kinds quantum informational tasks and quantum error-correcting codes (QECCs) are powerful tools to fight various quantum noises. For standard QECCs physical systems have the same number of energy levels. Here we shall propose QECCs over mixed alphabets, i.e., physical systems of different dimensions, and investigate their constructions as well as their quantum Singleton bound. We propose two kinds of constructions: a graphical construction based a graph-theoretical object composite coding clique and a projection-based construction. We illustrate our ideas using two alphabets by finding out some 1-error correcting or detecting codes over mixed alphabets, e.g., optimal $((6,8,3))_{4^52^1}$, $((6,4,3))_{4^42^2}$ and $((5,16,2))_{4^32^2}$ code and suboptimal $((5,9,2))_{3^42^1}$ code. Our methods also shed light to the constructions of standard QECCs, e.g., the construction of the optimal $((6,16,3))_4$ code as well as the optimal $((2n+3,p^{2n+1},2))_{p}$ codes with $p=4k$.