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 entangled vectors, (4) orthonormal bases of unitary operators with respect to the Hilbert-Schmidt scalar product and (5) depolarizing operations, whose Kraus operators can be chosen to be unitary. The teleportation. and dense coding schemes are assumed to be 'tight' in the sense that all Hilbert spaces involved have the same finite dimension d, and the classical channel involved distinguishes d(2) signals. A general construction procedure for orthonormal bases of unitaries, involving Latin squares and complex Hadamard matrices is also presented.