Fig. 1

a In our ancilla-assisted protocol, a null daemonic gain gain [i.e., \(\delta {\cal W}\) = 0, cf. Eq. (5)] implies the absence of quantum correlations between the system S and the ancilla A [as measured by the discord associated with measurements on S, cf. Eq. (6)]. b A non-null value of \(\delta {\cal W}\), on the other hand, implies the possible existence of quantum correlations between S and A. For pure bipartite states (in arbitrary dimensions), the nullity of the daemonic gain is a necessary and sufficient condition for separability