We discuss single-shot decoding of quantum Calderbank-Shor-Steane codes with faulty syndrome measurements. We state the problem as a joint source-channel coding problem. By adding redundant rows to the code's parity-check matrix we obtain an additional syndrome error correcting code which addresses faulty syndrome measurements. Thereby, the redundant rows are chosen to obtain good syndrome error correcting capabilities while keeping the stabilizer weights low. Optimal joint decoding rules are derived which, though too complex for general codes, can be evaluated for short quantum codes.

翻译：我们讨论了具有错误综合征测量的量子Calderbank-Shor-Steane码的所谓单次解码问题。我们将该问题表述为联合信源信道编码问题。通过向码的校验矩阵添加冗余行，我们获得了一个额外的用于处理错误综合征测量的综合征纠错码。因此，所添加的冗余行在保持稳定子重量较低的同时，被选择用以获得良好的综合征纠错能力。本文推导了最优联合解码规则，尽管这些规则对于一般码而言过于复杂，但仍可针对短量子码进行评估。