  We present a procedure inspired by dense coding, which enables a highly
efficient transmission of information of a continuous nature. The procedure
requires the sender and the recipient to share a maximally entangled state. We
deal with the concrete problem of aligning reference frames or trihedra by
means of a quantum system. We find the optimal covariant measurement and
compute the corresponding average error, which has a remarkably simple close
form. The connection of this procedure with that of estimating unitary
transformations on qubits is briefly discussed.
