MiS Preprint Repository

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 $\frac{1}{2}$ 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.