  We study entanglement and fidelity of a two-qubit system when a noisy
holonomic, non-Abelian, transformation is applied to one of them. The source of
noise we investigate is of two types: one due to a stochastic error
representing an imprecise control of the fields driving the evolution; the
other due to an interaction between the two near qubits. The peculiar level
structure underlying the holonomic operator leads us to introduce the reduced
logical entanglement which is the fraction of entanglement in the logical
space. The comparison between entanglement and fidelity shows how they are
differently affected by the noise and that, in general, the first is more
robust than the latter. We find a range of physical parameters for which both
fidelity and reduced logical entanglement are well preserved.
