In this work, we prove that quantum error correcting codes do not fix isotropic errors (Theorem 5), even assuming that their correction circuits do not introduce new errors. We say that a quantum code does not fix a quantum computing error if its application does not reduce the variance of the error. We also prove for isotropic errors that, if the correction circuit of a quantum code detects an error, the corrected logical m-qubit has uniform distribution (Theorem 3) and as a result, it already loses all the computing information.

中文翻译：

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量子代码不能解决各向同性误差

在这项工作中，我们证明了量子误差校正代码不能固定各向同性误差（定理5），即使假设其校正电路没有引入新的误差也是如此。我们说，如果量子代码的应用不能减小误差的方差，那么它就不能解决量子计算错误。对于各向同性错误，我们还证明，如果量子码的校正电路检测到错误，则校正后的逻辑m -qubit具有均匀的分布（定理3），结果，它已经失去了所有计算信息。