  We consider a realistic setting of quantum tasks that generate shared
bipartite quantum states. Suppose \alice and \bob are located at different
places and need to produce a target shared quantum state $\rho$. In order to
save quantum communication, they can choose to share a proper smaller quantum
state $\sigma$ first, and then turn $\sigma$ to $\rho$ by performing only local
quantum operations and classical communications (LOCC). We hope $\sigma$ is the
optimal such that the quantum communication needed is as little as possible,
which is called the generation cost of $\rho$. In this paper, for an arbitrary
bipartite $\rho$, we characterize its generation cost completely by proving
that it is exactly equivalent to the logarithm of the Schmidt number of $\rho$.
Similar quantum schemes where classical communication is not allowed have
actually been considered. By comparing the two settings, we are able to look
into the role that classical communication plays in these fundamental tasks,
where we exhibit some instances in which classical communication is not helpful
completely.
