Optimal strategies for sending information through a quantum channel

We present optimal encoding-decoding procedures for sending the information contained in an arbitrary direction (unit vector) using a quantum channel. We find that the maximal fidelity is given solely in terms of the dimension of the encoding space by F=d/(d+1). To attain this bound one has to use a codification somewhat difficult to implement physically. Encoding through (space) rotations is easier to realize, and in this case we prove that the maximal fidelity for arbitrary number of spins is directly related to the largest zeros of the Legendre and Jacobi polynomials. We show that this fidelity approaches unity quadratically in the number of spins. We also discuss our results in terms of the information gain