We analyze the entanglement measure $C_4$ for mixed states in general and for the transverse XY model. We come to the conclusion that it cannot serve alone for guaranteeing an entanglement of $GHZ_4$-type. The genuine negativity calculated in Ref.~cite{Hofmann14} isnt sufficient for that either and some additional measure of entanglement must be considered. In particular we study the transverse XY-model and find a non-zero $C_4$ measure which is of the same order of magnitude than the genuine negativity. Furthermore, we observe a feature in the $C_4$ values that resembles a destructive interference with the underlying concurrence.
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