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Given a quantum channel it is possible to define the non-commutative operatorgraph whose properties determine a possibility of error-free transmission ofinformation via this channel. The corresponding graph has a straight definitionthrough Kraus operators determining quantum errors. We are discussing theopposite problem of a proper definition of errors that some graph correspondsto. Taking into account that any graph is generated by some POVM we give asolution to such a problem by means of the Naimark dilatation theorem. Usingour approach we construct errors corresponding to the graphs generated byunitary dynamics of bipartite quantum systems. The cases of POVMs on the circlegroup ${\mathbb Z}_n$ and the additive group $\mathbb R$ are discussed. As anexample we construct the graph corresponding to the errors generated bydynamics of two mode quantum oscillator.

On errors generated by unitary dynamics of bipartite quantum systems