A Triangle Governs Genuine Tripartite Entanglement

TL;DR

This paper introduces a novel measure for genuine tripartite entanglement based on the area of a concurrence triangle, revealing new insights and advantages over existing measures in three-qubit systems.

Contribution

It proposes a new tripartite entanglement measure derived from a geometric constraint, demonstrating its superiority and highlighting differences with other measures.

Findings

The new measure is more effective in quantifying tripartite entanglement.

It reveals inequivalence between different entanglement measures.

The measure is interpreted geometrically as a triangle area.

Abstract

A previously overlooked constraint for the distribution of entanglement in three-qubit systems is exploited for the first time and used to reveal a new genuine tripartite entanglement measure. It is interpreted as the area of a so-called concurrence triangle and is compared with other existing measures. The new measure is found superior to previous attempts for different reasons. A specific example is illustrated to show that two tripartite entanglement measures can be inequivalent due to the high dimensionality of the Hilbert space.