  We introduce a notion of nuclear numerical range defined as the set of
expectation values of a given operator $A$ among normalized pure states, which
belong to the nucleus of an auxiliary operator $Z$. This notion proves to be
applicable to investigate models of quantum noise with block-diagonal structure
of the corresponding Kraus operators. The problem of constructing a suitable
quantum error correction code for this model can be restated as a geometric
problem of finding intersection points of certain sets in the complex plane.
This technique, worked out in the case of two-qubit systems, can be generalized
for larger dimensions.
