Impossibility via W states and feasibility via W-like states for perfect quantum teleportation

In this paper, we examine the two-party perfect quantum teleportation of an unknown 1-qubit state in the case of sharing various 3-qubit entangled states between a sender and a receiver: GHZ state, W state and W-like state. We give an impossibility proof that the W state cannot be used as the sharing state to realize the perfect quantum teleportation for transmitting an arbitrary 1-qubit state, in sharp contrast with the GHZ state which is well known to realize the perfect quantum transportation. Moreover, we give a procedure of obtaining a modified entangled state which we call the W-like state to achieve the perfect quantum transportation under a prescribed measurement basis.