  Recently, Harrow et al. [Phys. Rev. Lett. 92, 187901 (2004)] gave a method
for preparing an arbitrary quantum state with high success probability by
physically transmitting some qubits, and by consuming a maximally entangled
state, together with exhausting some shared random bits. In this paper, we
discover that some states are impossible to be perfectly prepared by Alice and
Bob initially sharing those entangled states that are superposed by the ground
states, as the states to be prepared. In particular, we present a sufficient
and necessary condition for the states being enabled to be exactly prepared
with probability one, in terms of the initial entangled states (maybe
nonmaximally) superposed by the ground states. In contrast, if the initially
shared entanglement is maximal, then the probabilities for preparing these
quantum states are smaller than one. Furthermore, the lower bound on the
probability for preparing some states are derived.

Quantum Physics