Average skew information-based coherence and its typicality for random quantum states

TL;DR

This paper derives explicit formulas for average skew information-based coherence in random quantum states, revealing their typical values and bounds, with pure states approaching maximum coherence and mixed states having lower average coherence as dimension increases.

Contribution

It provides the first explicit formulas for average skew information-based coherence for random pure and mixed states, and analyzes their typicality and bounds in high-dimensional spaces.

Findings

Average coherence approaches 1 for random pure states as dimension increases.

Average coherence for mixed states converges to a positive constant less than 1/2.

A coherent subspace exists where coherence can be bounded from below almost always.

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 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.