  Given a large number N of copies of a qubit state of which we wish to
estimate its purity, we prove that separable-measurement protocols can be as
efficient as the optimal joint-measurement one if classical communication is
used. This shows that the optimal estimation of the entanglement of a two-qubit
state can also be achieved asymptotically with fully separable measurements.
Thus, quantum memories provide no advantage in this situation. The relationship
between our global Bayesian approach and the quantum Cramer-Rao bound is
discussed.
