  It is known that quantum discord might experience a sudden transition in its
dynamics when calculated for certain Bell-diagonal states (BDS) that are in
interaction with their surroundings. We examine this phenomenon known as the
sudden change of quantum discord, considering the case of two qubits
independently interacting with dephasing reservoirs. We first numerically
demonstrate that, for a class of initial states which can be chosen arbitrarily
close to BDS, the transition is in fact not sudden, although it might
numerically appear so if not studied carefully. Then, we provide an extension
of this discussion covering the X-shaped density matrices. Our findings suggest
that the transition of quantum discord might be sudden only for an highly
idealized zero-measure subset of states within the set of all possible initial
conditions of two qubits.
