Characterization of Tripartite Quantum States with Vanishing Monogamy Score

TL;DR

This paper explores the conditions under which three-party quantum states have a zero discord monogamy score, revealing their entanglement structure and differences from entanglement-based monogamy measures.

Contribution

It provides necessary and sufficient conditions for vanishing discord monogamy score in pure states and analyzes their entanglement properties and Bell inequality violations.

Findings

States with zero discord monogamy score have limited genuine multipartite entanglement.

Pure states with vanishing discord monogamy score exhibit a distinct classification from concurrence-based monogamy.

The study reveals a rich structure in three-qubit states related to discord monogamy.

Abstract

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.