Necessary and sufficient conditions on n-qudit state for perfect teleportation of an arbitrary single qudit state

Firstly, we investigate the necessary and sufficient conditions that an entangled channel of n-qubits should satisfy to carry out perfect teleportation of an arbitrary single qubit state and dense coding. It is shown that the sender can transmit two classical bits of information by sending one qubit. Further, the case of high-dimension quantum state is also considered. Utilizing n  -qudit state as quantum channel, it is proposed that the necessary and sufficient conditions are (d+2)(d-1)2 in all to teleport an arbitrary single qudit state. The sender can transmit 2log2d2log2d classical bits of information to the receiver conditioned on the constraints.