  For a general tripartite system in some pure state, an observer possessing
any two parts will see them in a mixed state. By the consequence of
Hughston-Jozsa-Wootters theorem, each basis set of local measurement on the
third part will correspond to a particular decomposition of the bipartite mixed
state into a weighted sum of pure states. It is possible to associate an
average bipartite entanglement ($\bar{\mathcal{S}}$) with each of these
decompositions. The maximum value of $\bar{\mathcal{S}}$ is called the
entanglement of assistance ($E_A$) while the minimum value is called the
entanglement of formation ($E_F$). An appropriate choice of the basis set of
local measurement will correspond to an optimal value of $\bar{\mathcal{S}}$;
we find here a generic optimality condition for the choice of the basis set. In
the present context, we analyze the tripartite states $W$ and $GHZ$ and show
how they are fundamentally different.
