  The method of complementary channel for analysis of reversibility
(sufficiency) of a quantum channel with respect to families of input states
(pure states for the most part) are considered and applied to Bosonic linear
(quasi-free) channels, in particular, to Bosonic Gaussian channels.
  The obtained reversibility conditions for Bosonic linear channels have clear
physical interpretation and their sufficiency is also shown by explicit
construction of reversing channels. The method of complementary channel gives
possibility to prove necessity of these conditions and to describe all reversed
families of pure states in the Schrodinger representation.
  Some applications in quantum information theory are considered.
  Conditions for existence of discrete classical-quantum subchannels and of
completely depolarizing subchannels of a Bosonic linear channel are obtained in
the Appendix.
