Abstract
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 -qubit controlled teleportation are open to cheating; Alice and Bob may teleport -qubits of quantum information, out of the controllers' control. We conjecture that the straightforward protocol for controlled teleportation, which requires each controller to hold entangled qubits, is optimal. We prove this conjecture for a limited, but interesting, subset of protocols.