  We show that a generic $N$-qudit pure quantum state is uniquely determined by
only $2$ of its $\lceil\frac{N+1}{2}\rceil$-particle reduced density matrices.
Therefore we give a method to uniquely determine a generic $N$-qudit pure state
of dimension $D=d^N$ with $O(D)$ local measurements, which is an improvement
comparing with the previous known approach using $O(D\log^2 D)$ or $O(D\log D)$
measurements.
