Maximally entangled three-qubit states via geometric measure of entanglement

TL;DR

This paper characterizes maximally entangled three-qubit states using a generalized Schmidt decomposition and geometric measure, revealing a family of states that interpolate between GHZ and W states with distinct entanglement properties.

Contribution

It introduces a single-parameter family of maximally entangled three-qubit states based on geometric measures, connecting GHZ and W states as extreme cases.

Findings

GHZ and W states are extreme members of the family.

Different entanglement measures show opposite monotonic trends.

A unified characterization of three-qubit entanglement is provided.

Abstract

Bipartite maximally entangled states have the property that the largest Schmidt coefficient reaches its lower bound. However, for multipartite states the standard Schmidt decomposition generally does not exist. We use a generalized Schmidt decomposition and the geometric measure of entanglement to characterize three-qubit pure states and derive a single-parameter family of maximally entangled three-qubit states. The paradigmatic Greenberger-Horne-Zeilinger (GHZ) and W states emerge as extreme members in this family of maximally entangled states. This family of states possess different trends of entanglement behavior: in going from GHZ to W states the geometric measure and the relative entropy of entanglement and the bipartite entanglement all increase monotonically whereas the three-tangle and bi-partition negativity both decrease monotonically.