  Given a quantum channel it is possible to define the non-commutative operator
graph whose properties determine a possibility of error-free transmission of
information via this channel. The corresponding graph has a straight definition
through Kraus operators determining quantum errors. We are discussing the
opposite problem of a proper definition of errors that some graph corresponds
to. Taking into account that any graph is generated by some POVM we give a
solution to such a problem by means of the Naimark dilatation theorem. Using
our approach we construct errors corresponding to the graphs generated by
unitary dynamics of bipartite quantum systems. The cases of POVMs on the circle
group ${\mathbb Z}_n$ and the additive group $\mathbb R$ are discussed. As an
example we construct the graph corresponding to the errors generated by
dynamics of two mode quantum oscillator.
