  We consider the problem of broadcasting quantum information encoded in the
displacement parameter for an harmonic oscillator, from N to M>N copies of a
thermal state. We show the Weyl-Heisenberg covariant broadcasting map that
optimally reduces the thermal photon number, and we prove that it minimizes the
noise in conjugate quadratures at the output for general input states. We find
that from two input copies broadcasting is feasible, with the possibility of
simultaneous purification (superbroadcasting).
