Characterization of tripartite quantum states with vanishing monogamy score

Quantum discord, an information-theoretic quantum correlation measure, can satisfy as well as violate monogamy for three-party quantum states. We quantify the feature using the concept of discord monogamy score. We find a necessary condition of a vanishing discord monogamy score for arbitrary three-party states. A necessary and sufficient condition is obtained for pure states. We prove that the class of states having a vanishing discord monogamy score cannot have arbitrarily high genuine multipartite entanglement, as quantified by generalized geometric measure. In the special case of three-qubit pure states, their classification with respect to the discord monogamy score reveals a rich structure that is different from that which had been obtained by using the monogamy score corresponding to the entanglement measure called concurrence. We investigate properties like genuine multipartite entanglement and violation of the multipartite Bell inequality for these states.