Quantum entanglement and teleportation assisted by multiple parties

Quantum teleportation can be performed if and only if a message is combined with a maximally entangled state. Bennett et al. originally claimed this feasibility condition. In this paper, I give a proof of that condition. Moreover, I specify the condition for teleportation when a single-qubit message is combined with a three-qubit state distributed among three parties. I also consider the situation that a single-qubit message is combined with an $n$-qubit state distributed among $n$ parties.