  Several protocols for controlled teleportation were suggested by Yang, Chu,
and Han [PRA 70, 022329 (2004)]. In these protocols, Alice teleports qubits (in
an unknown state) to Bob iff a controller allows it. We view this problem in
the perspective of secure multi-party quantum computation. We show that the
suggested entanglement-efficient protocols for $m$-qubit controlled
teleportation are open to cheating; Alice and Bob may teleport $(m-1)$-qubits
of quantum information, out of the controllers' control. We conjecture that the
straightforward protocol for controlled teleportation, which requires each
controller to hold $m$ entangled qubits, is optimal. We prove this conjecture
for a limited, but interesting, subset of protocols.
