We present a universal framework for quantum error-correcting codes, i.e., a framework that applies to the most general quantum error-correcting codes. This framework is based on the group algebra, an algebraic notation associated with nice error bases of quantum systems. The nicest thing about this framework is that we can characterize the properties of quantum codes by the properties of the group algebra. We show how it characterizes the properties of quantum codes as well as generates some new results about quantum codes.

中文翻译：

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量子纠错码通用框架

我们提出了一个通用的量子纠错码框架，即一个适用于最通用的量子纠错码的框架。该框架基于群代数，这是一种与量子系统的良好误差基础相关的代数符号。这个框架最好的一点是，我们可以通过群代数的特性来表征量子代码的特性。我们展示了它如何表征量子代码的特性并产生一些关于量子代码的新结果。