All teleportation and dense coding schemes

We establish a one-to-one correspondence between (1) quantum teleportation schemes, (2) dense coding schemes, (3) orthonormal bases of maximally entan gled vectors, (4) orthonormal bases of unitary operators with respect to th e Hilbert-Schmidt scalar product and (5) depolarizing operations, whose Kra us operators can be chosen to be unitary. The teleportation. and dense codi ng schemes are assumed to be 'tight' in the sense that all Hilbert spaces i nvolved have the same finite dimension d, and the classical channel involve d distinguishes d(2) signals. A general construction procedure for orthonor mal bases of unitaries, involving Latin squares and complex Hadamard matric es is also presented.