对角量子信道的纠错码空间的存在性与构造

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.

Existence and Construction of Error-correcting Code Spaces of Diagonal Quantum Channels

We propose the concept of a diagonal quantum channel (DQC) by using the Kraus operators of a quantum channel and prove some properties of DQCs.It is proved that a quantum channel is a DQC if and only if it makes every diagonal matrix unchanged;all condensed matrices of a DQC have the same rank;a DQC is uncorrectable if and only if its condensed matrices are of full rank,and a DQC is correctable on the whole space if and only if its condensed matrices are of rank one.Finally,we give a constructing method of the code space of a DQC by using a concrete example.