  We identify optimal measurement strategies for phase estimation in different
scenarios. For pure states of a single qubit, we show that optimal measurements
form a broad set parametrized with a continuous variable. When the state is
mixed this set reduces to merely two possible measurements. For two qubits, we
focus on the symmetric Werner state. We find an optimal measurement and show
that estimation from the population imbalance is optimal only if the state is
pure. Finally, for a pure state of $N$ qubits, we finds under which conditions
the estimation from the full $N$-body correlation and from the population
imbalance are optimal.
