Average entropy of a subsystem over a global unitary orbit of a mixed bipartite state

TL;DR

This paper studies the average entropy of a subsystem over a global unitary orbit of a mixed bipartite state, providing bounds and exact formulas for von Neumann and linear entropies, with applications to correlation estimation.

Contribution

It offers an analytical lower bound for the average entropy of a subsystem and derives an exact formula for the average linear entropy in this context.

Findings

Derived an analytical lower bound for average subsystem entropy.

Obtained an exact formula for average linear entropy.

Applied results to estimate average correlation in the orbit.

Abstract

We investigate the average entropy of a subsystem within a global unitary orbit of a given mixed bipartite state in the finite-dimensional space. Without working out the closed-form expression of such average entropy for the mixed state case, we provide an analytical lower bound for this average entropy. In deriving this analytical lower bound, we get some useful by-products of independent interest. We also apply these results to estimate average correlation along a global unitary orbit of a given mixed bipartite state. When the notion of von Neumann entropy is replaced by linear entropy, the similar problem can be considered also, and moreover the exact average linear entropy formula is derived for a subsystem over a global unitary orbit of a mixed bipartite state.