  The quantum cost is a key ingredient to evaluate the quality of quantum
protocols from a practical viewpoint. We show that the quantum cost of
d-dimensional dense coding protocol is equal to d+3 when transmitting the
classical message (0,0), and that is equal to d+4 when transmitting other
classical message. It appears linear growth with the dimension and thus makes
sense for implementation. In contrast, the quantum cost of high-dimensional
teleportation protocols is equal to 13, which is the maximum value of the cost
for the two-dimensional case. As an application, we establish the relation
between the quantum cost and fidelity of dense coding protocols in terms of
four typical noise scenario.
