We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
99/2019
Average skew information-based coherence and its typicality for random quantum states
Zhaoqi Wu, Lin Zhang, Shao-Ming Fei and Xianqing Li-Jost
Abstract
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.
