Average coherence and its typicality for random mixed quantum states

TL;DR

This paper derives compact formulas for the average coherence and subentropy of random mixed quantum states modeled by the Wishart ensemble, advancing understanding of quantum state properties.

Contribution

It introduces a matrix integral technique to compute average coherence and subentropy for induced random mixed states, extending previous results.

Findings

Derived a formula for average coherence of random mixed states.

Obtained a compact expression for average subentropy.

Extended previous theoretical work with new integral techniques.

Abstract

Wishart ensemble is a useful and important random matrix model used in diverse fields. By realizing induced random mixed quantum states as Wishart ensemble with the fixed-trace one, using matrix integral technique we give a fast track to the average coherence for random mixed quantum states induced via partial-tracing of the Haar-distributed bipartite pure states. As a direct consequence of this result, we get a compact formula of the average subentropy of random mixed states. These obtained compact formulae extend our previous work.