Analytic Expressions for Geometric Measure of Three Qubit States

TL;DR

This paper introduces a new algebraic method to derive explicit formulas for the geometric measure of entanglement in three-qubit pure states, including W-states and symmetric states, with implications for quantum communication.

Contribution

It develops an explicit algebraic approach to compute the geometric entanglement measure for broad classes of three-qubit states, expanding analytical tools in quantum entanglement analysis.

Findings

Derived explicit algebraic equations for geometric entanglement

Solved equations for key classes like W-states and symmetric states

Discussed physical applications to quantum teleportation and superdense coding

Abstract

A new method is developed to derive an algebraic equations for the geometric measure of entanglement of three qubit pure states. The equations are derived explicitly and solved in cases of most interest. These equations allow oneself to derive the analytic expressions of the geometric entanglement measure in the wide range of the three qubit systems, including the general class of W-states and states which are symmetric under permutation of two qubits. The nearest separable states are not necessarily unique and highly entangled states are surrounded by the one-parametric set of equally distant separable states. A possibility for the physical applications of the various three qubit states to quantum teleportation and superdense coding is suggested from the aspect of the entanglement.