We investigate the sum uncertainty relations based on metric-adjusted skew information. By means of the norm property, we propose new uncertainty relations for arbitrary finite $n$ observables and arbitrary finite $N$ quantum channels via metric-adjusted skew information. Since Wigner-Yanase-Dyson skew information and Wigner-Yanase skew information are two special kinds of metric-adjusted skew information, our results are applicable to the above two special cases. The uncertainty relations obtained by us are tighter than the existing ones. Detailed examples are given.

中文翻译：

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通过度量调整的偏斜信息更紧密的总和不确定性关系

我们基于度量调整的偏斜信息研究总和不确定性关系。通过范数性质，我们通过度量调整的偏斜信息为任意有限$n$ 可观察物和任意有限$N$ 量子通道提出了新的不确定性关系。由于 Wigner-Yanase-Dyson 偏斜信息和 Wigner-Yanase 偏斜信息是两种特殊的 metric-adjusted 偏斜信息，因此我们的结果适用于上述两种特殊情况。我们得到的不确定性关系比现有的更紧密。给出了详细的例子。