  Let two coordinate systems, in possession of Alice and Bob, be related to
each other by an unknown rotation $R\in SO(3)$. Alice is to send identical
states $|\psi_0\ra$ to Bob who will make measurements on the received state and
will determine the rotation $R$. The task of Bob is to estimate these
parameters of the rotation $R$ by the best possible measurements. Based on the
Quantum Fisher Information, we show that Greenberger-Horne-Zeilinger (GHZ)
states are near optimal states for this task. Compared to the optimal states
proposed before, the advantage of $GHZ$ states are that they can be more easily
prepared experimentally, and more importantly, we show concrete measurements
which will allow Bob to determine the rotation $R$. We also study the
robustness of these states in keeping their encoded information, against common
sources of noises.
