  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.
