We investigate the total variance of a quantum state with respect to a complete set of mutually complementary measurements and its relation to the Brukner-Zeilinger invariant information. By summing the variances over any complete set of mutually unbiased measurements and general symmetric informationally complete measurements respectively, we show that the Brukner-Zeilinger invariant information associated with such types of quantum measurements is equal to the difference between the maximal variance and the total variance obtained. These results provide an operational link between the previous interpretations of the Brukner-Zeilinger invariant information.

中文翻译：

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互补测量中的总方差和不变信息

我们研究了量子态相对于一组完整的互补测量的总方差及其与 Brukner-Zeilinger 不变信息的关系。通过分别对任何完整的相互无偏测量集和一般对称信息完备测量集的方差求和，我们表明与此类量子测量相关的 Brukner-Zeilinger 不变信息等于最大方差与获得的总方差之间的差. 这些结果提供了先前对 Brukner-Zeilinger 不变信息的解释之间的操作联系。