A quantum code of a quantum system S is an arbitrary non-empty subset C of the set D( H ) of all density operators on complex Hilbert space H that describes the system S ,a quantum channel of S is a completely positive and trace preserving linear map ε on B(H ) .Some properties of noiseless quantum codes are researched and the relationships of strongly preserved code ,weakly preserved code and noiseless codes are obtained .It is proved that when the image of a code C under a quantum channel ε is contained in the fixed-point set of ε ,C is a noiseless code of ε if and only if C is weakly preserved by ε .For an arbitrary quantum channel ε and a quantum code C ,it is also proved that C is a noiseless code of ε if and only if it is a noiseless code of any convex combination of ε and ε2 .Lastly ,a weakly preserved code and a noiseless code of a quantum channel of the quantum system C2 ? C2 are presented .%量子码是描述量子系统的Hilbert空间H上一些密度算子之集,量子信道是C*-代数B(H)上的完全正保迹映射.本文揭示了无噪音量子码的一些性质,得到了强 、弱保护码与无噪音码的关系.证明了:当量子码C在量子信道 ε下的像包含在ε的不动点之集时,C为ε的无噪音码当且仅当C被ε弱保护;对于任一量子信道 ε 及量子码C,证明了C为ε的无噪音码当且仅当C为ε与ε2的任意凸组合的无噪音码,还给出量子系统C2?C2的一个量子信道的弱保护码与无噪音码.
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