  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.
