The complementarity (upper bound) and uncertainty relations (lower bound) of the coherence via skew information under mutually unbiased bases (MUBs) are studied. The complementarity relation for the geometric measure of coherence is also obtained based on the relation between the coherence via skew information and the geometric measure of coherence. As applications, two tighter upper bounds are presented on the minimum error probabilities that discriminate a set of pure states with the least square measurement, which improve the results of Xiong et al. (Phys Rev A 98:032324, 2018).

中文翻译：

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在相互无偏的条件下通过偏态信息进行量子相干的应用

研究了在互不偏基（MUB）下通过偏斜信息的相干性的互补性（上界）和不确定性关系（下界）。还基于通过偏斜信息的相干性与相干性的几何度量之间的关系，获得了相干性的几何度量的互补关系。作为应用，在最小误差概率上给出了两个更严格的上限，这些最小误差概率用最小二乘测量值来区分一组纯状态，从而改善了Xiong等人的结果。（Phys Rev A 98：032324，2018）。