对角量子信道纠错码空间的存在性与构造

发布时间：2018-02-23 20:40

本文关键词： 对角量子信道纠错码空间压缩矩阵秩　出处：《数学学报(中文版)》2017年04期 　论文类型：期刊论文

【摘要】：通过量子信道的Kraus算子,提出了对角量子信道的概念,证明了对角量子信道的一些性质:一个量子信道成为对角量子信道的充要条件是所有对角矩阵都是它的不动点;同一对角量子信道的所有压缩矩阵具有相同的秩;一个对角量子信道不可纠错的充要条件是其压缩矩阵是行满秩的.进而证明了一个对角量子信道在整个空间上可纠错当且仅当其压缩矩阵为1秩阵.最后,利用一个具体例子给出了构造对角量子信道的码空间的一种方法.
[Abstract]:Through the Kraus operator of quantum channel, the concept of diagonal quantum channel is proposed, and some properties of diagonal quantum channel are proved: if and only if a quantum channel becomes a diagonal quantum channel, all diagonal matrices are its fixed points; All compression matrices of the same pair of angular quantum channels have the same rank; It is proved that a diagonal quantum channel is error-correcting in the whole space if and only if its contraction matrix is a rank matrix. Finally, it is proved that a diagonal quantum channel is error-correcting if and only if it is a 1-rank matrix. A method of constructing the code space of diagonal quantum channel is given by an example.
【作者单位】：陕西师范大学数学与信息科学学院;
【基金】：国家自然科学基金资助项目(11401359,11371012,11571211,11571213)
【分类号】：O177

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