We study the average skew information-based coherence for both random pure and mixed states. The explicit formulae of the average skew information-based coherence are derived and shown to be the functions of the dimension N of the state space. We demonstrate that as N approaches to infinity, the average coherence is 1 for random pure states, and a positive constant less than 1/2 for random mixed states. We also explore the typicality of average skew information-based coherence of random quantum states. Furthermore, we identify a coherent subspace such that the amount of the skew information-based coherence for each pure state in this subspace can be bounded from below almost always by a fixed number that is arbitrarily close to the typical value of coherence.

我们研究随机纯态和混合态的平均基于偏度信息的相干性。推导了基于平均偏斜信息的相干性的显式公式，并显示为状态空间维数N的函数。我们证明，当N接近无穷大时，随机纯态的平均相干性为1，而随机混合态的平均相干性小于1/2。我们还探讨了基于平均偏度信息的随机量子态相干性的典型性。此外，我们确定了一个连贯的子空间，以便该子空间中每个纯态的基于偏度信息的连贯性的数量几乎总是可以从下面限制为一个固定数值，该数值任意接近于连贯性的典型值。