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It is known that quantum discord might experience a sudden transition in itsdynamics when calculated for certain Bell-diagonal states (BDS) that are ininteraction with their surroundings. We examine this phenomenon known as thesudden change of quantum discord, considering the case of two qubitsindependently interacting with dephasing reservoirs. We first numericallydemonstrate that, for a class of initial states which can be chosen arbitrarilyclose to BDS, the transition is in fact not sudden, although it mightnumerically appear so if not studied carefully. Then, we provide an extensionof this discussion covering the X-shaped density matrices. Our findings suggestthat the transition of quantum discord might be sudden only for an highlyidealized zero-measure subset of states within the set of all possible initialconditions of two qubits.

Sudden change of quantum discord for a system of two qubits