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We find that when a qubit initialized in a pure state experiences puredephasing due to interaction with an environment, separable qubit-environmentstates generated during the evolution also have zero quantum discord withrespect to the environment. What follows is that the set of separable stateswhich can be reached during the evolution has zero volume and hence, sucheffects as sudden death of qubit-environment entanglement are very unlikely. Incase of the discord with respect to the qubit, a vast majority of separablestates qubit-environment is discordant, but in specific situations zero-discordstates are possible. This is conceptually important since there is a connectionbetween the discordance with respect to a given subsystem and the possibilityof describing the evolution of this subsystem using completely positive maps.Finally, we use the formalism to find an exemplary evolution of an entangledstate of two qubits that is completely positive, occurs solely due tointeraction of only one of the qubits with its environment (so one could guessthat it corresponds to a local operation, since it is local in a physicalsense), but which nevertheless causes the enhancement of entanglement betweenthe qubits. While this simply means that the considered evolution is completelypositive, but does not belong to LOCC, it shows how much caution has to beexercised when identifying evolution channels that belong to that class.

Equivalence of qubit-environment entanglement and discord generation via pure dephasing interactions and the consequences thereof