Classification of three-qubit genuine entangled states using concurrence fill

TL;DR

This paper introduces the use of concurrence fill, a geometric measure, to classify three-qubit genuine entangled states, providing a more operational and tractable approach than previous measures.

Contribution

It reformulates concurrence fill using three tangle and partial tangles, enabling effective classification of GHZ and W states, including mixed states.

Findings

Derived a classification criterion for GHZ and W states using concurrence fill.

Analyzed rank-2 mixtures of GHZ and W states, providing bounds for mixed states.

Reformulated concurrence fill for practical computation in multipartite entanglement.

Abstract

Despite the successful experimental generation and verification of genuine multipartite entanglement, several existing entanglement measures remain insufficient to reliably capture its presence. In this study, we overcome this challenge by utilizing a geometric measure known as concurrence fill, which quantifies genuine multipartite entanglement of pure states using the area associated with the underlying concurrence triangle. Firstly, the concurrence fill for three-qubit pure states is reformulated using three tangle and partial tangles. This yields a representation that is more tractable and operational. Using this formulation, we derive a criterion to classify GHZ and W class of states. Next, we analyse the rank-2 mixture of generalized GHZ and W class of states for which three-tangle is known to vanish over a zero polytope. Furthermore, we derive the concurrence fill for the eigenstates of the corresponding mixture and obtain its upper bound for mixed states with zero tangle.