A geometric formulation to measure global and genuine entanglement in three-qubit systems

TL;DR

This paper presents a geometric approach to quantify and control global and genuine entanglement in three-qubit systems using entanglement-polytopes, enabling manipulation of entanglement properties.

Contribution

It introduces a novel geometric formulation for measuring and controlling entanglement in tripartite qubit systems based on entanglement-polytopes.

Findings

Defines measures for global and genuine entanglement using eigenvalues of reduced states

Provides a method to manipulate entanglement by solving the inverse problem

Offers a framework for practical entanglement control in quantum systems

Abstract

We introduce a purely geometric formulation for two different measures addressed to quantify the entanglement between different parts of a tripartite qubit system. Our approach considers the entanglement-polytope defined by the smallest eigenvalues of the reduced density matrices of the qubit-components. The measures identify global and genuine entanglement, and are respectively associated with the projection and rejection of a given point of the polytope on the corresponding biseparable segments. Solving the so called `inverse problem', we also discuss a way to force the system to behave in a particular form, which opens the possibility of controlling and manipulating entanglement for practical purposes.