Controlled Dense Coding with Symmetric State

Two schemes, introducing the projective operator and the auxiliary qubit respectively, for controlled dense coding are investigated by using a three-qubit symmetric state with entanglement, where the supervisor (Cliff) can control an average amount of information transmitted from the sender (Alice) to the receiver (Bob) by adjusting the measurement angle θ. We show that the results for the average amounts of information are unique from the different two schemes. The schemes may be extended to many-qubit systems.