  A model of quantum noisy channel with input encoding by a classical random
vector is described. An equation of optimality is derived to determine a
complete set of wave functions describing quantum decodings based on
quasi-measurements maximizing the classical amount of transmitted information.
A solution of this equation is found for the Gaussian multimode case with input
Gaussian distribution. It is described by the overcomplete family of coherent
vectors describing an optimal quasimeasurement of the canonical annihilation
amplitudes in the output Hilbert space. It is found that the optimal decoding
in this case realizes the maximum amount I=Spln[1+S/(N+1)] of the classical
information as transmitted via the classical Gaussian channel with the
effective noise covariance matrix N+I. A physical realization of optimal
quasi-measurement based on an indirect (heterodyne) observation of the
canonical operators is suggested.
