  We consider error correction, based on the theory of non-commutative graphs,
for a model of a qubit interacting with quantum oscillator. The dynamics of the
composite system is governed by the Schr\"odinger equation which generates
positive operator-valued measure (POVM) for the system dynamics. We construct a
quantum channel generating the non-commutative graph as a linear envelope of
the POVM. The idea is based on applying a generalized version of a quantum
channel using the apparatus of von Neumann algebras. The results are analyzes
for a non-commutative graph generated by a qubit interacting with quantum
oscillator. For this model the quantum anticlique which determines the error
correcting subspace has an explicit expression.
