This paper proves that any quantum t-deletion-correcting codes also correct a total of t insertion and deletion errors under a certain condition. Here, this condition is that a set of quantum states is defined as a quantum error-correcting code if the error spheres of its states are disjoint, as classical coding theory. In addition, this paper proposes the quantum indel distance and describes insertion and deletion errors correcting capability of quantum codes by this distance.

翻译：本文证明，在特定条件下，任何量子t-删除纠错码也能纠正总计t个插入和删除错误。此处所述条件为：若一组量子态的误差球互不相交，则将其定义为量子纠错码，这与经典编码理论中的定义一致。此外，本文提出了量子插入删除距离，并利用该距离描述了量子码对插入和删除错误的纠错能力。