An algebraic approach to the study of multipartite entanglement

TL;DR

This paper introduces an algebraic method and specific functionals for analyzing multipartite entanglement in pure states, reproduces known results, and characterizes GHZ-states as the only states maximizing certain entanglement measures across all bipartitions.

Contribution

It presents a novel algebraic framework and functionals for studying multipartite entanglement, providing new insights into the structure of maximally entangled states.

Findings

Functionals are connected to purity.

Maximization of entanglement functionals is only compatible with GHZ-states.

Reproduction of known entanglement results using the algebraic approach.

Abstract

A simple algebraic approach to the study of multipartite entanglement for pure states is introduced together with a class of suitable functionals able to detect entanglement. On this basis, some known results are reproduced. Indeed, by investigating the properties of the introduced functionals, it is shown that a subset of such class is strictly connected to the purity. Moreover, a direct and basic solution to the problem of the simultaneous maximization of three appropriate functionals for three-qubit states is provided, confirming that the simultaneous maximization of the entanglement for all possible bipartitions is compatible only with the structure of GHZ-states.